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Calculus/Questions Answered by Expert Scotto
| Subject | Date Asked |
| Request for answers onQuantitative Analysis for Managerial Applications | 2/8/2012 |
| Q: Sir, Please help me solve the questions given below. I will be ever grateful to you. 1. Solve ... A: 1. Solve the following simultaneous equations by using Cramer’s rule 3x+2y=13 2x-y=4 Cramer's Rule: ... | |
| Pre-Calc question | 2/5/2012 |
| Q: Can you help me with parts (b) and (c) of the following question? The price of an item is initially ... A: a) After 4 years, the value will have gone up by $120, so it will be worth $820. To get an equation, ... | |
| calculus question | 1/31/2012 |
| Q: wondering if you could help me with this question, PART A). Find 5 nonzero terms of Fourier Series ... A: Yes, the attached graph made the 1st answer very clear. PART A By looking at the graph, non-zero ... | |
| Algorithm | 1/31/2012 |
| Q: Instructions: Given the gallons of gasoline used and the starting miles and the ending miles, ... A: starting mileage 1200 ending mileage 1290 gallons used 6 mileage = (end - start)/used = ... | |
| Calculus | 1/5/2012 |
| Q: Suppose r(x)=x^2/(x^2+1) represents revenue and c(x)= (x-1)^3/3-1/3 represents cost, with x measured ... A: Since profit is revenue minus cost, we have p(x) = r(x) - c(x) = [x²/(x²+1)] - [(x-1)³/3 - 1/3]. At ... | |
| calculus | 12/21/2011 |
| Q: find the coordinates of the points on the curve y=2-cosx/sinx in the range 0<x<2pi where the ... A: If the curve is y = 2 - cosx/sinx, then that is y = 2 - ctnx. However, I believe it really to be y ... | |
| Quotient Rule | 12/17/2011 |
| Q: I've been given the function f(x)=x^(2/3)(x-5) and by using product rule came up with the first ... A: Since we have f'(x) = g(x)/h(x), we know that f"(x) = [h(x)g'(x) - g(x)h'(x)]/h²(x). Since g(x) = ... | |
| calculus | 12/14/2011 |
| Q: suppose a spring has a natural length of 8 inches to extend the spring 2 inches a force of 3 pounds ... A: It is known that for springs, E = FK, where ... E is the displacement, and that is 2", F is the ... | |
| Implicit Differentiation | 12/3/2011 |
| Q: Could you please help me solve tan(xy)=xy with implicit differentiation? I got the derivative: ... A: What is left to do is solve for dy/dx. That is, we have sec²(xy)y + sec²(xy)(dy/dx) = y + x(dy/dx). ... | |
| calculus | 11/30/2011 |
| Q: Find the equation of the slant asymptote for the function, f(x)=(x^2+1)/(x+1) A: I somehow didn't remember what an assymptote was until now. I believe the slope is undefined since ... | |
| Convexity and increasing character | 11/25/2011 |
| Q: I am an Italian boy with a school and university curriculum in humanities, who is trying to ... A: -f is strictly convex if and only if f' is strictly increasing; Note that f'(x) is also the slope ... | |
| calculus | 11/24/2011 |
| Q: The following diagram below shows part of the graph of f(x)=5-x^2 with vertex V(0,5). Its image ... A: The vertex is currently at (0,5). To shift the vertex to (3,6), note that the change is x is from 0 ... | |
| Archery Variation Sport (angular Velocity) | 11/21/2011 |
| Q: Do you feel this variation of Archery game can be introduced as a Good Olympics Sport in future ? ... A: Yes, archery sounds like a good game for the Olympics. They could introduce several varieties, just ... | |
| Applied Calculus for Business | 11/17/2011 |
| Q: Can you help with finding the derivative of a function and leaving the answer in its simplest form ... A: The derivative of Ax^N with A,N as constants, x as the variable is ANx^(N-1). That is, if we have ... | |
| calvulus | 11/17/2011 |
| Q: The average speed of a vehicle on a stretch of Route 134 between 6 a.m. and 12 p.m. on a typical ... A: In most questions I have seen, the capital letter function is the integral of the lower case letter ... | |
| Optimization | 11/16/2011 |
| Q: My problem is as follows... A storage box with a square base must have a volume of 80 cubic ... A: The box has a square base that is x cm wide. The volume is the width • depth • height, and this is ... | |
| area under a curve | 11/16/2011 |
| Q: Scotto! I have searched the entire internet to answer this simplewhat is the TOTAL area under the ... A: So, 2011 - 37 = 1972, and that is when my oldest brother started college, but I was coming out of ... | |
| Releated rates, race car approaches camera | 11/14/2011 |
| Q: You are videotaping a race from a stand 132ft from the track. You are following a car racing at ... A: The relation is given by tanA = x/y, where the track is y feet away, the distance of the car from ... | |
| Calculus | 11/12/2011 |
| Q: answer to a is r=(t+1)*.25 answer to b is 80 5. At time , the volume of a sphere is increasing at ... A: We are given dV/dt = C/r, for some constant C. It is known that V(t) = 4πr³(t)/3. When t=0, ... | |
| math-calculus | 11/11/2011 |
| Q: Four cities are exactly located at the each end of square land with side 1mile. I want to connect ... A: I would draw an X with the roads, having a city at each of the four endpoints on the X. The length ... | |
| Pre-Calc | 11/11/2011 |
| Q: 1. Simplify: 1 - cos^4x / sin^2x 2. Prove Identity sinx tanx + cosx = secx 3. Evaluate all 6 trig ... A: 1. Simplify: 1 - cos^4x / sin^2x It can be said that 1 - cos^4x = (1-cos²x)(1+cos²x) and that sin²x ... | |
| Calculus Optimization | 11/7/2011 |
| Q: The function, f(x)= 6(x+1)^-1 is graphed in the first quadrant and a tangent line is drawn at the ... A: The slope is the derivative, f'(x). Since f(x) = 6/(x+1), f'(x) = -6/(x+1)². The point x0 that is ... | |
| linearly independent quadratic polynomials | 10/29/2011 |
| Q: for a set of n quadratic polynomials qi(x)=ai(x^2) +bi(x) +c,s.t n>3,is it possible that not exist ... A: From what I read, this is very similar to what I wrote, but more to the point. You're saying for a ... | |
| linearly independent quadratic polynomials | 10/27/2011 |
| Q: for a set of n quadratic polynomials qi(x)=ai(x^2) +bi(x) +c,s.t n>3,is it possible that not exist ... A: Let me rewrite the equation as Q(x)*d = Q0(x)*d0 + Q1(x)*d1 + .... + Q(n-1)(x)*d(n-1). and ... | |
| Derivatives - Quotient Rule (Homework Help) | 10/27/2011 |
| Q: I just have a question from my textbook that I'm having trouble with. Find the derivative of: ... A: When f(x) = hi/low, the derivative is (low d hi - hi d low)/low². I remember this equation as the ... | |
| Cacluls | 10/24/2011 |
| Q: How to solve the b) question?? Mind to guide me?? and what you get for the final answer ?? Thanks ^^ A: Integrating with respect to z gives 4xyz. Evaluating from x downto 0 gives 4x²y - 0 = 4x²y. ... | |
| Cacluls | 10/23/2011 |
| Q: whats the answer you get for 4(a)(i),(ii) and (iii) ?? Just wanna compare..I dun have the ans :( A: I don't have the 'd' symbol for partial derivatives, so I will use df/dx to mean the partial ... | |
| Squeeze Theorem | 10/22/2011 |
| Q: I am busy preparing for my Calculus examination by working through previous question papers. I have ... A: 1. The only problem on the 1st question is in the line -1 < sin(1/h) < 1, it should really read -1 < ... | |
| finding the derivative | 10/20/2011 |
| Q: I am having a bit of trouble finding the first and second derivative of the function f(x)=xe^x I ... A: The derivative follows the product rule. If we have f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + ... | |
| Calculus | 10/19/2011 |
| Q: Sketch a graph of a function that has all of the following properties: A) f'(x)>0 when x<-1 and ... A: Now if you want one that satisfies all of the properties together, start with f"(x). Take f"(x) = ... | |
| engineering | 10/13/2011 |
| Q: For the following signals, which are periodic, if periodic give the period and sketch the signal ! ... A: I can't sketh the signal, but can say that sin(x) and cos(x) have a period of 2π. They have a ... | |
| Calculus equation to the tangent line | 10/12/2011 |
| Q: Consider the function y=f(x)=e^(2x) Find an equation to the line tangent to the graph of the ... A: The derivative of e^(2x) is like the derivative of e^f(x), where f(x) = 2x. Given that f(x) = 2x, ... | |
| limit of a square root | 10/12/2011 |
| Q: I don't understand what to do with this question. find the lim as x goes to 4 of (the square root of ... A: This sounds like find lim(x->4)[√(x+5) - 3)/(x-4). When x=4 is put in, we get (√9 - ... | |
| derviatives | 10/11/2011 |
| Q: 1) Write the equation of the line tangent to the curve y= 3x^3 - 2x at the point where x=2 2) ... A: 1) Put x=2 into the equation to find the value for y, and I believe you'll get y=20. Find dy/dx and ... | |
| calulus 1 | 10/9/2011 |
| Q: heres my question each side of an equilateral triangle is changing at a constant rate of 30 ... A: The area is A = s²√3/4, and ds/dt = 30 cm/min. It can be seen that dA/dt = ... | |
| Calculus Differentiation and percentage rate of change? | 10/7/2011 |
| Q: In each of these cases, find the percentage rate of change of the function f(t) with respect to t at ... A: a) If the function is f(t) = (t²)(3-2t)³, then this is f(t) = a(t)b(t). The derivative is f'(t) = ... | |
| Calculus | 10/5/2011 |
| Q: Find the slope of the curve when Y = 2 given e^x(y^2) + (y^3) - 8 = 2x Thanks :-) A: To find the slope, we need to find y'. Since the derivative of e^x is e^x, and the 1st term's ... | |
| calculus | 10/2/2011 |
| Q: hai,, can u help me in my report..tnx.. here is the given.. each side of an equilateral triangle is ... A: The area of an equilateral triangle is A(3)= s²√3/4. Note that only the 3 is under the ... | |
| Pre-Cal | 9/30/2011 |
| Q: Good evening. i was trynig to get some help on this problem. Im getting confused. ... A: The interval of usage must be given in the problem. The x-values are the values in this interval. ... | |
| Solving usi)ng Definition of Derivative | 9/29/2011 |
| Q: I have the following question on a homework assignment from my Calc 110 class, really struggling to ... A: Let a be close to x. Since x = 1, a could be like 0.9. It was given that f(x) = 3, and it f(0.9) ... | |
| partial differentiation | 9/23/2011 |
| Q: I want to ask when is partial derivative applied?Is it when there is a function of more than one ... A: Use of Differential Equations ----------------------------------------------------------- When ... | |
| Pre-calculus | 9/22/2011 |
| Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time ... A: It splashes down when h(t) = 0. This is a quadratic equation with a=-4.9, b=227, and c=353, and the ... | |
| partial differentiation | 9/20/2011 |
| Q: I want to ask when is partial derivative applied?Is it when there is a function of more than one ... A: The Master's paper I wrote in college dealt with partial derivatives. It was on the effect of shock ... | |
| Negative divided by Zero plus | 9/15/2011 |
| Q: Hey, I've been looking all over the place for an answer to this question but I just can't find it. ... A: Yes, that is the correct answer. The best thing to know is that no question is too simple. If ... | |
| calculus derivatives | 9/13/2011 |
| Q: e to the (1/x)? i got -xe(1/x) A: For e to the a, it is written as e^a. The function is f(x) = e^(1/x). The derivative is the chain ... | |
| Calculus | 9/12/2011 |
| Q: Given y = 1/(X-1) at x=2 find: a) slope b) equation of the tangent c) an equation of the normal d) ... A: Here, y = (x-1)^(-1). Since when y = x^n, y' = nx^(n-1), in this case, y' = -1(x-1)^(-2) = ... | |
| Algebraic Square, Cube Formulas / Equations. | 9/10/2011 |
| Q: We have the following formulas 1. (a + b)^2 = a^2 + 2ab + b^2 2. (a − b)^2 = a^2 − 2ab ... A: The way to do it with that special triangle. On the edges, the value is always 1. In the middle, it ... | |
| Derivative | 9/9/2011 |
| Q: Derivative of f(x)=-8x^5 sqrt(x) + -8/(x^2*Sqrt(x))? A: To take the derivative, first rewrite the equation. Since sqrt(x) = x^0.5 and 1/x = x^-1, we have ... | |
| Functions | 9/7/2011 |
| Q: f(x)=3x^2+2x-4 problem: f(x+1)=3(x+1)^2+2(x+1)-4 A: Is this suppose to be simplified? Note that (x+1)^2 = x^2 + 2s + 1, so when multiplied by 3 it ... | |
| Chain Rule. | 9/6/2011 |
| Q: If f(x)=x^2 and g(x)=|x|. (f o g)(x)=x^2 and (g o f)(x)=x^2. Both are differentiable at x=0. But the ... A: To be differentiable, a function must be continuous and smooth. The function g(x) is not smooth at ... | |
| Chain Rule. | 9/5/2011 |
| Q: If f(x)=x^2 and g(x)=|x|. (f o g)(x)=x^2 and (g o f)(x)=x^2. Both are differentiable at x=0. But the ... A: The function g(x) = |x| is not differentiable at x = 0, for one side has slope 1 and the other side ... | |
| Change in Y on the tangent line | 8/1/2011 |
| Q: Given: The curve is y=f(x), x starts out with a and then changes by the infinitesimal amount dx. ... A: The tangent line gives the slope of the curve at that point. For example, if y = x², then it can be ... | |
| Calculus help | 7/27/2011 |
| Q: A tin can (right circular cylinder) with top and bottom is to have volume V. What dimensions (the ... A: The volume of a can is V, with radius on the top and bottom of r, and height h. This gives equation ... | |
| Calculus | 7/25/2011 |
| Q: What are local maximum and minimum values and what does it mean when a question asks for a period if ... A: The maximum and minimum values are where the derivative is 0. For this problem, we have y = ... | |
| Calculus | 7/18/2011 |
| Q: can you please help me with another calculus problem, I have attached it as an image. Thank you so ... A: Polar coordinates will be used. It is known that the radius r = 1 and the angle A goes from 0 to ... | |
| Calculus | 7/17/2011 |
| Q: I am studying for the Pharmacy school exam and am struggling with this problem, can you please ... A: It can be seen that since f(x) = x²/6, then f(x) = 2²/6 = 4/6 = 2/3, and f(6) = 6²/6 = 6. The slope ... | |
| Preparing for AP Calculus AB | 7/4/2011 |
| Q: I'm taking AP Calculus AB in high school next year, and as I'm pretty worried about it, I'd like to ... A: You'll learn it in calculus, but there are only so many functions to deal with. What you'll learn ... | |
| calculus | 7/3/2011 |
| Q: Water is being drained from a pond such that the volume of water in (m^3) in the pond after t hours ... A: Yes it is. Sorry about that. It should read First, note that V(t) is given as 2(90 - t)^2. This ... | |
| calculus | 7/1/2011 |
| Q: Water is being drained from a pond such that the volume of water in (m^3) in the pond after t hours ... A: First, note that V(t) is given as 2(90 - t)^2. This means dV/dt = 2*2(90-t)^1. This is the same as ... | |
| Calculus (related rates) | 6/16/2011 |
| Q: I have a calculus problem. I left my notes at work so I have no idea how to do this one. Pleaese ... A: The area of a plate is A(t) = pi*r^2(t). From this, we differentiate and get dA/dt = ... | |
| maths | 6/13/2011 |
| Q: If f(x)/(x-1)the reminder is 5 and when divided by (x-2) the remainder is 7.What is the remainder ... A: Since (7-5)/[(x-1)-(x-2)] = 2/1, 2 is the number of times it divides. Since we are dividinbg by x-2 ... | |
| math. | 6/9/2011 |
| Q: I'm doing a potato lab: Newton's cooling effect. Here is myIf the initial temperature of the hot ... A: The constant would be the difference in temperature, K = 92.3 - 23.5. The equation for temperature ... | |
| Calculus preperation | 5/29/2011 |
| Q: my question isn't necessarily a homework one, but more of an academic circumstance in need of ... A: With your determination in taking both trig and college algebra in the same semester, and you're ... | |
| A few questions | 5/24/2011 |
| Q: I have a few quick questions for a homework worksheet I have to do. I believe I am doing them right ... A: 1. The number of answers is 55*54*53*52*51*50/(6*5*4*3*2*1) = 28,989,675 2. That would be ... | |
| calculus question: revolving a trig function | 5/21/2011 |
| Q: How do I find the volume of the solid generated by revolving the region bounded by the graphs of the ... A: The radius of a circle at any particular point is 8 - sin(x). The area of this circle is pi*r^2, so ... | |
| ARC LENGTH PROOF | 5/19/2011 |
| Q: I can't for the life of me see how the sume of the infintesimal lines on the curve translates into ... A: If you have a question asking for and integral of squareroot(1 + d^2y/dx^2) dx, that means to find ... | |
| calculus | 5/17/2011 |
| Q: plzzzzzzz clearly explain partial differentiation and countour integration A: Partial integration is done on a function of many variables with respect to only one varible. ... | |
| Pre-Calc Identities | 5/9/2011 |
| Q: I have difficulties answering these haha.. can you help me with one? Sin 4θ = (Cos θ)(4 ... A: Let's starte with (Cos θ)(4 sin θ - 8 sin^3 θ). A 4(sin Θ) can be factored out, ... | |
| Please, help me with a Calculus Problem | 5/8/2011 |
| Q: Jerry rent snowmobiles at a ski lodge. If the rental fee is $25 per half hour, Jerry knows he can ... A: The base is $25 each for 50 rentals, and that is $1,250. For each dollar he increases the fee by ... | |
| Calculus Help, Please! | 5/6/2011 |
| Q: I need help on this quickly please! A particle moves along a line so that its velocity at time t ... A: 1 The distance is the integral of velocity. That gives t^3/3 - 2t + C. At t=0, the position is C. At ... | |
| ARC LENGTH PROOF | 5/5/2011 |
| Q: I can't for the life of me see how the sume of the infintesimal lines on the curve translates into ... A: When finding the value of an integral, it finds the area of an infinite number of rectangle below ... | |
| Calculus | 5/4/2011 |
| Q: I have 2 question First An open rectangular box with square ends to hold 6400cu. ft. is to be built ... A: 1. The depth of the box is x. Since the ends are square, the height is x. Since the volume is 6,400, ... | |
| integration | 5/3/2011 |
| Q: what is L-hosptal rule and how it is used to evaluate limits of the form 0/0 ?plzzz explain clearly ... A: All problems can be differentiated by the power rule, exponential rule, or one of the trig rule ... | |
| percentages... | 4/29/2011 |
| Q: I have an item that I have scaled down to 60% it's original size. I want to scale it back up to it's ... A: I'm not sure such equipment can restore items to the original size. If something is taken from size ... | |
| The Slope of a Tangent Line at a Point | 4/28/2011 |
| Q: I am taking a calculas class from a nearby city over the internet, but have been given next to no ... A: The slope of a line is the value of the derivative. If F(x) = sqrt(x+2), that is the same as F(x) = ... | |
| Calculus: Related Rates | 4/27/2011 |
| Q: A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the ... A: The equation for surface area of a sphere is 4*pi*r^2. The change is found by the derivative times 8 ... | |
| Definite Integrals | 4/26/2011 |
| Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. ... A: If f(x) = 3x - 6, the integral, known as F(x) = 3(x^2)/2 - 6x and the answer would be F(3) - F(-1). ... | |
| limits | 4/21/2011 |
| Q: what is L-hosptal rule and how it is used to evaluate limits of the form 0/0 ?plzzz explain clearly ... A: Noy only is 0/0 involved, but infinity/infinity is involved as well. L'hospital's rule states that ... | |
| Calculus | 4/15/2011 |
| Q: Let r be the region in quadrant one enclosed by the graph of y=e^x and the line x=1. set up an ... A: Revolving a point on the graph around the x axis makes a circle at that s value. The left side is at ... | |
| Calculus | 4/13/2011 |
| Q: Veda is working on a formula that would help predict the possible damage of tidal waves in the ... A: a) Top find the instantaneous rate of change on h(R) at R=3, find h'(R) and input 3 for R. That is, ... | |
| Radians | 4/10/2011 |
| Q: Sorry for bothering you, but I asked you a question regarding the distance between the centres of ... A: It's OK, since I enjoy answering them. ... | |
| calculus | 4/6/2011 |
| Q: Prove the following properties of limits using the ε-d definition. Assume that lim as x tends ... A: 1. It is known that lim(x->a)(cf(x)) = c*lim(x->a)f(x), so that is c*K. 2. The lim(x->a)(f(x)+g(x)) ... | |
| Calculus | 4/4/2011 |
| Q: The volume of water in a bowl is given by V=1/3ph^2 (60 - h) cm^3, where h is the depth of the water ... A: Note that h is really h(t), so h' is h'(t). I right the equation as V(h) = ph²(60-h)/3 cm^3 and p ... | |
| Pre-calc question | 4/3/2011 |
| Q: I have no idea how to solve this. Please help. thank you A: It is known that sin(π/180) = -sin(359π/180), and this is term 1 and term 359. This ... | |
| calculus- maximum minimum- derivatives | 3/31/2011 |
| Q: I can't seem to figure out how to solve this equation...I know I need to remove some of the ... A: The radius of the circle is a, so the diameter is 2a. If the sides of the rectangle are b and c, ... | |
| f(x)= (x^2)(e^(-4x)) | 3/28/2011 |
| Q: (a) Find the x- and y-intercepts of the function. (b) Draw a number line for f: (c) Find all ... A: (a) The x-intercept is at x=0 and that is where y=0. (b) No range was given, so I used the numbers ... | |
| f(x)= sinx + 1 on [-2pi, 2pi] | 3/28/2011 |
| Q: (a) Find the x- and y-intercepts of the function. (b) Draw a number line for f: (c) Find all ... A: (a) Note that the minimum of a sin() curve is -1 at x=π ± 2nπ for n any integer. For the ... | |
| f(x)=x^3 - 3x^2 + x + 1 | 3/28/2011 |
| Q: (a) Find the x- and y-intercepts of the function. (b) Draw a number line for f: (c) Find all ... A: Looking at the coefficients, they are 1 -3 1 1, and the sum of those numbers is 1. That means that ... | |
| Sea Falcon Calculus question | 3/27/2011 |
| Q: 1. In a recent pretrial run for the world water water speed record, the velocity of Sea Falcon II t ... A: Since there are 4 intervals to be done on a width of 20, that would be 4 per interval Since the ... | |
| dagster calculus problem | 3/27/2011 |
| Q: The velocity of a dragster t seconds after leaving the starting line is v (t )=100t e−0.2t ... A: Since we know velocity, distance is the integral of velocity. That is, d(t) = integral(v(t). Since ... | |
| fencing optimization problem | 3/26/2011 |
| Q: A farmer has a rectangular pen, which he divides into 5 identical pig pens. Each of the five pig ... A: The best set up would be to put the 5 pens in a row. For the sides together, which I will refer to ... | |
| Calculus project | 3/18/2011 |
| Q: I am not sure how to start on this project. My professor mentioned we can use Maple or Mathlab. Can ... A: The surface area is (2*pi*R)(2*pi*r) where R is the radius of the circle that is on the outside of ... | |
| related rates | 3/14/2011 |
| Q: Certain Chemotherapy dosages depend on a patient's surface ares. According to Mosteller model S= sqr ... A: Let's assume that Tom is full grown and the height is constant, so the only variable is w. To find ... | |
| Limit's | 3/14/2011 |
| Q: Compute lim x->1 x^2-1/x^2+5x-6 algebraically with factoring and using l'Hopital's Rule A: Note that (x²-1)/(x²+5x-6) = [(x-1)(x+1)]/[x+6)(x-1)]. Cancelling the (x-1) terms on the top and the ... | |
| Implicit differentiation | 3/14/2011 |
| Q: Find dy/dx for the function xy+y^2-2x=o A: Think of y as some function of x (which it is), and then see that xy is a product rule and y² is a ... | |
| Business Calculus | 3/11/2011 |
| Q: Good afternoon, The question is to calculate the average rate of change [a,a+h] where ... A: ALl that is left to do is to put in a=5 for the 1st and a=2 for the 2nd with h as 1, 0.1, 0.01, and ... | |
| calculus | 3/9/2011 |
| Q: differentiate w.r.t x :e^1/2*x^1/2 ANSWER: The 1st term, e^(1/2), is √e, and that's a ... A: In the exponential function f(x) = e^x, e is a constant and is defined as e = 2.7182818245905... as ... | |
| calculus | 3/8/2011 |
| Q: differentiate w.r.t x :e^1/2*x^1/2 A: The 1st term, e^(1/2), is √e, and that's a constant. The 2nd term, x^(1/2), has a derivative ... | |
| Calculus | 3/2/2011 |
| Q: Let 4x^2+4x+xy=2 and y(2)=-11. Find y'(2) by implicit differentiation A: It is given that y(2) = -11. Checking this out gives 4(2^2) + 4(2) - 11(2) = 16 + 8 - 22 = 2, and ... | |
| calculus | 3/2/2011 |
| Q: The following if myf(x)= (x^2/3)/1+x+x^4 I am supposed to use a computer system to graph f, f prime, ... A: The denomiinator is 1+x+x^4, and where that is 0, there are inflection points. It is noted, however, ... | |
| Calculus Applications of Differentiation | 3/2/2011 |
| Q: a rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What ... A: Make a rectangle out of the fence that is A x B. Cut it in half from the middle of each side of ... | |
| calculus | 2/26/2011 |
| Q: The demand function and the cost function for x units of a product are p= 40/sqrt(x) and ... A: Using http://www.dummies.com/how-to/content/how-to-determine-marginal-cost-marginal-revenue-an.html ... | |
| calculus | 2/26/2011 |
| Q: I am taking college calc and am struggling with the cost functions!Thanks for any help! The manager ... A: The numeer of units will be taken as 120+x. The rent will then be 350-5x. The 5x is subtracted ... | |
| calculus | 2/26/2011 |
| Q: Im need help with cost functions. Im taking college level calc and I am really struggling! Any help ... A: If a 21 dollare rebate increases sales by 210, and p is assumed to be linear, that would be 10 TV's ... | |
| Integrals | 2/26/2011 |
| Q: Determine the value of ∫ from 1 to 0 du/[(1 + u^2)(1+ u). I have no idea how to do partial ... A: I believe by that you mean ∫(1 downto 0)1/[(1 + u²)(1+u)] du. Most of the time what is to the ... | |
| Calculus | 2/24/2011 |
| Q: . Let f be the function defined by f(x)=x³+ax²+bx+c and having the following properties. (I) ... A: Since f(x) = x³ + ax² + bx + c, it is known that f'(x) = 3x² + 2ax + b and that f"(x) = 6x + 2a. ... | |
| Word Problem | 2/23/2011 |
| Q: The country has $10 billion in paper currency in circulation, and each day $50 million comes into ... A: Note that 50 million out of 10 billion is the same as 50 out of a 10,000, which is is the same as ... | |
| Max/min | 2/21/2011 |
| Q: I'm trying to find the point (x,y,z) on the plane 2x-y+z=3 that is closest to the point (2,0,-1). I ... A: No, since 2(-5/7) - 18/7 + 13/7 = -15/7, whereas it should equal 3, which is 21/7. From what I can ... | |
| related rates | 2/20/2011 |
| Q: Let xy=2 and dy/dt=1. Find dx/dt when x=1. A: Note that dy/dt = y'(t) and dx/dt = x'(t). The problem should really be x(t)y(t) = 2, since x and y ... | |
| Calculus | 2/15/2011 |
| Q: A spherical balloon is being filled with helium at the rate of 9 ft^3/min. How fast is the surface ... A: The volume of a sphere is (4/3)pi*r^3. This is also 36pi ft^3/min, so r can be found. Also dV/dt = ... | |
| Sigma Notation | 2/13/2011 |
| Q: 592 Z (5k + 2j)= k=126 This is a summation problem. I'm stumped. HELP A: It is known that j is a variable and the total number of j's is always 2 every time, so the total is ... | |
| Calculus | 2/10/2011 |
| Q: How do you find the value of x where the extreme values of the function y=x^3-7x-5x occur? A: To find the derivative of f(x) = ax^n, df/dx = anx^(n-1). That is, just multiply by the exponet. To ... | |
| sinx/x is this a continous curve | 2/8/2011 |
| Q: When x = 0 is it true that sin(x)/x = 1 or is this just the case as x tends to zero. I feel the ... A: As x approaches 0, sin(x)/x approaches 1. It is not continuous at x = 0, but the limit does exist. ... | |
| Population Growth | 2/8/2011 |
| Q: The rate of growth of a populations of fruit flies is proportional to the size of the population at ... A: The number is Ax^n, where A is the number at day 0 and n is the number of days. We know that Ax^2 = ... | |
| Limits and functions | 2/7/2011 |
| Q: Prove that lim[x:->a] [(x^n +a^n)/(x-a)]=na^(n-1) A: Since the top and bottom of the fraction both go to 0, the derivative of the top and bottom can be ... | |
| Calculus II integration by parts | 2/6/2011 |
| Q: How should I compute this integral? What would be the answer? S (x^5)(cos^3(x^6)(sin^2(x^6)) dx A: The first thing to do is let u = x^6, so du = 6*x^5 dx. This is the samme as (1/6)du = x^5 dx. This ... | |
| Combination | 2/4/2011 |
| Q: Could you please help me with the following? Q. Eight cards are selected with replacement, from a ... A: Since there are 52 ways of secelecting each card, the answer to (a) is 52^8. Note that 52^2 = 2,704. ... | |
| Calculus Linearization of a Function at Small x - Taylor Series | 2/3/2011 |
| Q: In trying to refresh for a course in advanced math going back to my calc 2 Taylor Series math. ... A: To take the derivative of this function, the chain rule is involved repeated. First, we have the ... | |
| calculus | 2/3/2011 |
| Q: Identify u, du and the formula ∫du/√(a+bu)=1/√a ... A: It is customary to write the du at the end. The way you have it written with the du right after the ... | |
| Calculus | 1/31/2011 |
| Q: I’m stuck on these Calculus questions. 1. When a curve attains a maximum value, the slope of its ... A: 1. The slope of a smooth curve at the maximum or minimum is 0, so y' = 0. 2. Given y = -3x² + 12x, ... | |
| calculus | 1/31/2011 |
| Q: A meteorologist sketched the path of the jet stream on a map of the northern U.S. and southern ... A: If the path is y = 6[e^(0.02x)][sin(0.2x)], find y' to see where the maxes and mins are at. Once y' ... | |
| Calculus | 1/31/2011 |
| Q: A certain production process uses labor and capital. If the quantities of these commodities are x ... A: We are given that C = 200y + 100x where C is a cost that is suppose to be 600, 800, and 1000. ... | |
| calculus | 1/31/2011 |
| Q: The lowest flying speed v (in ft/s) at which a certain airplane can fly varies directly as the ... A: If it says it varies directly with the squareroot, that means at a velocity v and a weight w, v = ... | |
| Calculus | 1/27/2011 |
| Q: The cross sections of an irrigation canal are isosceles trapezoids of which three sides are 8 feet ... A: If the angle off horizontal is theta and the diagonal is 8, then the height is h = 8*sin(theta) and ... | |
| Derivatives | 1/23/2011 |
| Q: How fast is the surface area of a spherical balloon increasing when the radius is 10cm and the ... A: Since V and r are both functions of t, both sides are differentiated with respect to t. Definition ... | |
| Derivatives | 1/21/2011 |
| Q: How fast is the surface area of a spherical balloon increasing when the radius is 10cm and the ... A: It is known that the surface area is A = 4*pi*r^2. Since we want the change with respect to time of ... | |
| help with calc | 1/21/2011 |
| Q: How fast is the surface area of a spherical balloon increasing when the radius is 10cm and the ... A: It is known that the surface area is A = 4*pi*r^2. Since we want the change with respect to time of ... | |
| Derivatives | 1/21/2011 |
| Q: A rectanglular shet of metal of perimeter 36cm and dimensions x and y is to be rolled into a ... A: If we let the height = y, then x is the diameter of the base. Since 2*pi*r = x, r = x/(2*pi). The ... | |
| help | 1/20/2011 |
| Q: Let f be the function defined by f(x) = x.e^-x? a. Determine the y-intercept b. Determine the ... A: a. When x is 0, y is 0. b. There is a horizontal only, at x = 0. c. In this case, f(x) is a ... | |
| rate of change problem | 1/20/2011 |
| Q: sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the ... A: If the height is h, the diameter is also h. This means the radius is h/2. The volume of a cone is ... | |
| calculus | 1/20/2011 |
| Q: Approximate the value of the given intergral by completing part (a) and (b) (a) use the trapezoidal ... A: The trapezoidal rule says to compute the are of n trapezoids under the function. Since n = 4, they ... | |
| differentiation | 1/19/2011 |
| Q: what is the derivative of the nth power of absolute value of x?or simply derivative of absolute ... A: If f(x) = |x|, then f'(x) = 1 for x>0 and f'(x) = -1 for x < 0. At 0, f'(x) is not defined. From ... | |
| calculus | 1/18/2011 |
| Q: Find the average value of the function on the given interval; f(x)=e^x/4,[0,9] the textbook answer ... A: It looks like the right bracket was left out. It is really [F(9)-F(0)]/9, where the subtraction on ... | |
| calculus | 1/18/2011 |
| Q: Find the average value of the function on the given interval; f(x)=e^x/4,[0,9] the textbook answer ... A: To find the average, it is [F(9)-F(0)]/(9-0) = [F(9)-F(0)]/4. Now e^x is suppose to have priority ... | |
| calculus | 1/17/2011 |
| Q: Find the area bounded by y(x+5)=1,x=0,y=0,x=3 so far I have y=1/x+5 and x=3 I am stuck their . the ... A: The curve would be y = 1/(x+5), and would be integrated from 0 to 3. The function is always positive ... | |
| calculus | 1/16/2011 |
| Q: Find the first- quadrant area under the curve of; y= 4ln^x/x from x=1 to x=5 A: I believe the function is y = 4*ln(x)/x on x = 1 to x = 5. Since x is never 0 in the range 1 to 5, ... | |
| Calculus: related rates | 1/16/2011 |
| Q: A rectangle is inscribed in a circle of radius 5 inches. If the length of the rectangle is ... A: If the rectangle is inscribed in a circle, that means the corners touch the edge of the circle. If ... | |
| shapes of polynomials | 1/12/2011 |
| Q: Greetings Sir, When taking the taylor expansion of certain functions,for example e^x using ... A: The overall formula for approximating a function is sum(n=0..N)[f^n(x0)(x-x0)^n/n!]. That is, N is ... | |
| calculus | 1/9/2011 |
| Q: im having trouble with these questions: (i) Determine whether the function given by f(x; y) = xy ... A: (i) If the second partial derivatives are positve, it is a minimum, and if they are negative, it is ... | |
| Calculus-Related Rates | 1/8/2011 |
| Q: A cylindrical tank with height 15m and diameter 2m is being filled with gasoline at a rate of 500 ... A: To find out how fast it is rising, solve the equation Ah = 500,000 cm^3. Note that A is in cm^2 and ... | |
| volume&area | 1/7/2011 |
| Q: 1.how to derive the formulas of volumes of cylinder,cone&sphere?? 2.how to derive the formulas of ... A: Picture the cyllinder sideways with the center of each circle on the x axis. Since the area of a ... | |
| Calculus- | 1/7/2011 |
| Q: An object moves so that its velocity, v, is related to its position, s, according to v= square root ... A: If s is for seconds, accelaration is not a consant. If the velocity v = √(b² + 2ga) and b and ... | |
| volume&area | 1/6/2011 |
| Q: 1.how to derive the formulas of volumes of cylinder,cone&sphere?? 2.how to derive the formulas of ... A: 1. The volume a cylinder is the area of the base times the height. The area of the base is the area ... | |
| nature of the shape of curves | 1/5/2011 |
| Q: Greetings Sir, Is it possible to have two different cubic curves that have the same shape in a ... A: I have used several varieties of software for plotting curves, but that was back in the 90's. The ... | |
| Integration of Absolute Values | 1/4/2011 |
| Q: What is the definite integral of the absolute value of 2x-3 on the interval [0,3]? A: The function is 0 at 2x - 3 = 0. Add 3 to both sides and get 2x = 3, or x = 3/2. Since 3/2 is in ... | |
| delta process | 1/4/2011 |
| Q: I am stuck simplifying a equation. ∆y=(t+∆t)²-t²+8(t+∆t)-8t is the equation ... A: Now ∆ must be deltam but we'll just go with ∆. Multiplying the first one out gives t² + ... | |
| nature of the shape of curves | 1/4/2011 |
| Q: Greetings Sir, Is it possible to have two different cubic curves that have the same shape in a ... A: Without special definition for each section, I don't think so. If the two curves f(x) = x + 2 and ... | |
| rate of change | 1/2/2011 |
| Q: find the difference quotient and use it to find the average rate of change on the curve between the ... A: 1. If the first function is f(x) = 4x-5, and x goes from 2 to 9, then f(2) = 4*2 - 5 = 8 - 5 = 3, ... | |
| accuracy of log | 1/1/2011 |
| Q: Sir,i was wondering how calculate the accuracy of a number given its log approximation i.e if the ... A: If we know x is in (x-e,x+e) where e is the error term, then calculate ln(x+e) - ln(x-e) to get the ... | |
| Minimizing the piping | 1/1/2011 |
| Q: Can you answer this question for me? I can't illustrate this problem. There are some information ... A: It states that the two towns are 20 km apart on the same side of the river. It also states that the ... | |
| integration | 12/29/2010 |
| Q: i was hoping you could explain what the integral of 1/((u^2/4)+1) is and also the formula used. the ... A: Make a right triangle with the are side u/2, the near side 1, and the angle be A. This would make ... | |
| calculs | 12/19/2010 |
| Q: how can we find area of a irregular polygon with the help of calculus? A: Divide the polygon into regions where one line is at the top and one line is at the bottom. Once ... | |
| solve this problem | 12/12/2010 |
| Q: I do not get this problem can you solve this for me? If g(x, y) = √5xy − 7x , find gx ... A: If will assume the problem is g(x,y) = √(5xy) - 7x. To find gx and gy, take the partial ... | |
| Calculus | 12/8/2010 |
| Q: At what point on the graph of y = 1 + 1/x will the tangent line pass through the point (3,0)? A: The slope is the derivative of y. The derivative is f'(x) = -1/x^2. Solve the equation (y-3)/(x-0) ... | |
| calculus | 11/30/2010 |
| Q: Find the value of x for which the given function is increasing and those values of x for which it is ... A: The derivative is y' = 2x + 2. The derivative is 0 at 2x + 2 = 0, or 2x = -2, or x = -1. This means ... | |
| calculus | 11/30/2010 |
| Q: for the cubic: f(x) = ax^3+bx^2+cx+d, a is not zero, find conditions on a,b,c and d to ensure that: ... A: The slope is the derivative. This means the slope is 3ax^2 + 2bx + c. This can be solved for the two ... | |
| differential calculus | 11/22/2010 |
| Q: find the slope of a line tangent to the curve y=3x^2 at the point P (1.5,6.75)by finding the limit ... A: We are given x1 = 1, x2 = 1.4, x3 = 1.49, and x4 = 1.499. With these we get y1 = 3(1^2) = 2, y2 = ... | |
| Trigonometry(Math) | 11/21/2010 |
| Q: In Prince Albert, Saskatchewan, the sun rises at 09:17 on December21 and at 04:35 on June 22. ... A: Since there are 365 day in a year (365.25, to be technical about it). The period of a sin wave is ... | |
| differential calculus | 11/21/2010 |
| Q: Find the slope of a line tangent to the curve by=x^2 at the point P(3,9)by finding the limit of the ... A: Take the 1st x value as 3 and call is x1. It is known the 3^2 = 9. Take each of the x values as x2 ... | |
| calculus | 11/20/2010 |
| Q: 9^(x^2 +x)= 3^4 A: When 9 is taken to a power, it is the same as taking 3 to twice the power. For example, 8^2 = 81 ... | |
| Business calculus | 11/20/2010 |
| Q: I am sorry for the last message i sent professor, these are the revised questions. Determine the ... A: a) I believe the elasticity is given by the change in quantity over the change in price. b) Yes, to ... | |
| Calculus (LIMITS) | 11/20/2010 |
| Q: I want the proof of lim x->a+=lim x->a- A: This proof is not always true. If this proof is true on f(x), then f(x) is said to be continuous at ... | |
| diferential calculus | 11/19/2010 |
| Q: Find the slop of a line tangent to the curve y=2x^2 at the point P(2.5,12.5) by finding the limit of ... A: Looking at, "Find the slop of a line tangent to the curve y = 2x^2 at the point P(2.5,12.5) by ... | |
| Business calculus | 11/19/2010 |
| Q: I am sorry for the last message i sent professor, these are the revised questions. Determine the ... A: Find extreme points of f(x) = -x^3 - 9x^2 - 24x - 2 To find the extremum, find the derivative and ... | |
| calculus | 11/17/2010 |
| Q: find the volume of the region D cut from the sphere x^2+Y^2+z^2=1 by the cylinder x^2+(y-.5)^2=.25 A: The sphere is centered at (0,0,0) and has radius 1. The cylinder is center on a line with x=0 and ... | |
| maximize revenue | 11/12/2010 |
| Q: A 150-room resort hotel is filled at a room rate of $125 per day. For each $5 increase in the room ... A: Since the increase is $5 and the decrease is 3 rooms, let n be the variable. This gives the rental ... | |
| critical points and abs max and min | 11/8/2010 |
| Q: find all critical points, and the absolute maximum and absolute minimum, of the function f(x)= ... A: The derivative of the function is f'(x) = (10/3)/x^(1/3) - (5/3)x^(2/3). This is the same as f'(x) ... | |
| Calculus | 11/8/2010 |
| Q: limit as x approaches 0 sec(x) -1 / e^2x - 2x -1. Determine all points where the curve x^4=x^2y-y^3 ... A: The value at 0 if (sec(x) -1)/(e^2x - 2x - 1) is 0/0, so I believe it is L'hospital's rule that says ... | |
| Summation | 11/8/2010 |
| Q: Can you please show me how the summation of sin(pi*j)/j, where j=-n to n equals pi? Thank you A: It is known that sin(πj) = 0 anytime j is an integer. This means the summation is ... | |
| Calculus | 11/7/2010 |
| Q: A leaky cylindrical oilcan has a diameter of 4 inches and a height of 6 inches. The can is full of ... A: (a) Since the diameter of the cone is the same as the depth, and the diameter of the cone is known ... | |
| Limits | 11/6/2010 |
| Q: Problem: lim x->inf (x)(sin(pi/x)) I have tried l'hospital's rule / squeeze the book answer is ... A: First, I will rewrite the problem. Take it as lim(x->infinity)[sin(pi/x)]/[(1/x)]. We now have ... | |
| related rates | 10/18/2010 |
| Q: A lighthouse is located on a small island 5 km away from the nearest point P on a straight ... A: This sound like a right triangle. The distance out to the light house is 5 km. The distance on the ... | |
| nth derivatives and induction | 10/17/2010 |
| Q: 1. The problem statement, all variables and given/known data proving the nth derivative of x to the ... A: Sometimes it is better to just deal with the problem at the start. It almost looks like the ... | |
| AP Calculus | 10/16/2010 |
| Q: I am trying to solve for the five variables in this equation. However, I have only three points. I ... A: There are more equations here than is first seen. To be a local minimum, it must solve F'(x) = 0 and ... | |
| related rates of a triangle | 10/15/2010 |
| Q: A triangle's Height is growing at 2.5cm/min while its area is growing at 7cm^2/min. At what rate is ... A: When the area of a triangle is 42 cm^2 and the height is 18 cm, that means A = bh/2 with b as base ... | |
| Calc 160 | 10/14/2010 |
| Q: im asked to differentiate y=(5x-5)^3(3-x^4) after using the chain rule and product rule i get ... A: Let f(x) = (5x-5)^3 and g(x) = 3-x^4; The result would be y' = fg' + gf'. Now f'(x) = 15(5x-5)^2 and ... | |
| Calculus | 10/12/2010 |
| Q: Differentiate 1.5 x (square root of Xcubed) - (4 divided by X) A: Find f'(x) is f(x) = 1.5√x³ - 4/x. To rewrite f(x) with powers, note that the squareroot of a ... | |
| Integration problem | 10/9/2010 |
| Q: Please tell me is the following integration correct and can you explain how is it possible (please ... A: No, the is not correct since the derivative of ln(f(s)) = f'(s)/f(s). Now the ... | |
| MS-08: Quantitative Analysis for Managerial Applications | 10/6/2010 |
| Q: 3. From a set of 1000 observations known to be normally distributed, the mean is 534 cm and SD is ... A: Use the normal table mathsisfun.com/data/standard-normal-distribution-table.html the number between ... | |
| mathematics | 10/3/2010 |
| Q: A spherical balloon is blown up so that its volume increases at a constant rate of 2cm cube per ... A: We will assume the volume is a sphere. This makes the volume V(t) = 4(pi)r^3(t)/3. The derivative ... | |
| calc ab | 9/30/2010 |
| Q: how do I use the definition to take the derivative of 1/((x+3)^1/2 )? A: The definition says if f(x) = x^n, the derivative is f'(x) = nx^(n-1). For this case, we have x+3 ... | |
| Math/Physics | 9/23/2010 |
| Q: I'm supposed to use the quadratic equation for the following physics problem: A bus has stopped to ... A: Assuming the equation is right, then 10 + 5t = 0.5*t². That is the same as 10 + 5t = t²/2. Putting ... | |
| absolute value limits | 9/22/2010 |
| Q: f(x) = { |x^3 - 4x| x<1 x^2 - 2x - 2 x>=1 A: To consier x<1, the function has the value |x³ - 4x|. This means take any x value and put into the ... | |
| rewriting logarithmic equations | 9/22/2010 |
| Q: How do i rewrite the expression as the logarithm of a single quantity? 1/2[ln(x+1)+2ln(x-1)]+3lnx A: If the equation is [ln(x+1) + 2*ln(x-1)]/2 + 3lnx, this become ln(x+1)/2 + ln(x-1) + 3ln(x). ... | |
| Calc Homework | 9/20/2010 |
| Q: When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, ... A: I will refer to Q(subscript 0) as Q0. a) If Q(t) = Q0(1-e^(-t/a)), then to find the inverse, solve ... | |
| Estimating | 9/17/2010 |
| Q: what is an adjusted estimate? A: An adjustment to an estimate is the new value that is gotten when the parameters that give it are ... | |
| Calculus | 9/16/2010 |
| Q: I have term in this fashion C=(A/B)*(second derivative of some function). If B is greater than A is ... A: Then if C is a contanst as well as B and A, CB/A is a contant. In this case, V = CBx/A + D and S = ... | |
| Calculus | 9/15/2010 |
| Q: I have term in this fashion C=(A/B)*(second derivative of some function). If B is greater than A is ... A: If the function is C = (A/B)*f"(x) for some f(x), and A, B, and C are all constants, then B>A ... | |
| Related Rates | 9/14/2010 |
| Q: A rectangle is inscribed in a circle of radius 5 inches. If the length of the rectangle is ... A: If the rectangle is inscribed in a circle of radius 5 and has one side that measures 6, draw this on ... | |
| Calculus | 9/14/2010 |
| Q: The limit as t approaches zero-- 1 1 -------------- - ---- t[sqrt(1 + t)] ... A: The problem says to find lim(t->0) [1/{t[sqrt(1 + t)]} - 1/t]. The denominators can be made the ... | |
| Right Prism | 9/14/2010 |
| Q: in the figure is shown a block of wood in the form of a right prism whose bases are right triangles. ... A: Find the height on the block of the center of the cyllinder. Find the length at that height. ... | |
| Right Prism | 9/13/2010 |
| Q: in the figure is shown a block of wood in the form of a right prism whose bases are right triangles. ... A: The length of the hole at the base is 8". The length of the hole 2" up is 8" - 4/3 of the distance ... | |
| Confusing Word Problem | 9/12/2010 |
| Q: Suppose a professor counts the final exam as being equal to each of the other tests in her course, ... A: Test 1 81 81 81 81 81 Test 2 63 63 63 63 63 Test 3 51 51 51 51 51 Test 4 90 90 90 90 90 ... | |
| trig/physics | 9/10/2010 |
| Q: The Sun sets, fully disappearing over the horizon as you lie on the beach, your eyes 30cm above the ... A: Put this in triangle format. The first triangle has a side that is 6,378,100 m and a hypotenuse ... | |
| curved surface of the cone | 9/10/2010 |
| Q: A & B are diametrically opposite points on the base of a cone of semi-vertical angle 35 degrees, ... A: Slant height is the diagonal height, and that is 6 inches. Now if h is the height and r is the ... | |
| partial derivative | 9/9/2010 |
| Q: I need to find a partial derivative of this function, vanderwaals gas equation: ... A: This reminds me of the equation pV = nrt, no? Here, p, V, and r could all be functions of time with ... | |
| solving logarithmic function | 9/9/2010 |
| Q: [0.99*ln(1,000,000+x)]+[0.01*ln(900,000+x)]=13.8155. Solve for x. These are utility functions asking ... A: I did it in Excel and approximated it until I got an error of 0. Now the erroor of 0 is not really ... | |
| Pre-Calculus | 9/9/2010 |
| Q: What are the possible rational roots of 3x^3 - 2x^2 + 6x - 7 =0? Factor x^3 - 8x^2 + 17x - 6 ... A: Try x-1 as a factor. This gives (x-1)(3x^2 + x + 7), and that looks right. Take a=3, b=1, and c=7. ... | |
| solving logarithmic function | 9/8/2010 |
| Q: [0.99*ln(1,000,000+x)]+[0.01*ln(900,000+x)]=13.8155. Solve for x. These are utility functions asking ... A: Since the second term would be much smaller than the first, solve ln(1,000,000+x) = 13.8155. Do this ... | |
| circular cylinder | 9/8/2010 |
| Q: a circular cylinder is inscribed in a right circular cone of altitude h and radius of base x, as ... A: Let the cone have radius on the base of r. Let the cyllinder have radius on the circle at the base ... | |
| Calc | 9/7/2010 |
| Q: how do i solve -3x^3+x+4=2.05 A: I would solve it using Excel. Note that this is the same as 3x^3-x-1.95=0. In A1 put a guess for x ... | |
| Pre-Calculus | 9/6/2010 |
| Q: cubed root 3 radical 16x^4 - cubed root 3 radical 2x A: Take cr(x) as cube root of x. It is known that cr(16)=cr(8)cr(2) and cr(8)=2, so cr(16) = 2cr(2). ... | |
| Confused | 9/5/2010 |
| Q: I have this question that says perform the indicated opertations and simplify: x-4/x+1 - 5/x^2+x A: I would first combine the fractions. Note that the 1st fraction needs to be multiplied by (x^2 + ... | |
| Calculus 3 | 9/5/2010 |
| Q: Determine whether the points lie on a straight line, a, A(2,4,2) B(3,7,-2) C(1,3,3) b, D(0,-5,5) , ... A: Take the points each asw (x,y,z). Look at the difference in the x values. For the set in a, the x ... | |
| differentiation | 9/3/2010 |
| Q: An architect plans to build a triangular enclosure with a fence on two sides and a wall on the third ... A: Let A be the angle. Cut A in half and form a right triangle with the fence of length L and the half ... | |
| calculus | 9/2/2010 |
| Q: Consider the curve √x + √y =1,for x,y ≥ 0. Show that the sum of the x-and ... A: Let the point on the curve be (a,b). Now the curve is √x + √y = 1, so √y = 1 - ... | |
| Pyramids | 8/30/2010 |
| Q: Any help would be awesome thanks, the problem goes like this what fraction of the volume of a ... A: The volume of a pyramid is Ah/3 where A is the area of the base and h is the height. The area of ... | |
| Maxed out on ODE but calculus your okay? | 8/6/2010 |
| Q: WOW! Simple request this time. Please verify dy/dx=2A/3v I get ... A: What equation is being looked at that needs this solution? The solutin to y" + y' + Ey = 0 for some ... | |
| Sequence and Series | 8/5/2010 |
| Q: The Common difference of an Arithmetic progression is 2 and the common ratio of a geometric ... A: The first terms of the AP is A and the GP is G. This means A + G = 8. The 2rd term is two terms ... | |
| Calc | 8/5/2010 |
| Q: Consider an infinite series of the form (+-)3(+-)1(+-)1/3(+-)1/9(+-)1/27(+-)....(+-)1/3^n(+-)... ... A: Note that 3 to powers is 3, 9 (3^2), 27 (3^3), 81 (3^4), 243 (3^5), etc. This will be used later. ... | |
| summation-integration | 8/4/2010 |
| Q: sir, what is the proof that riemann summation(limit n --> infinity, sigma i=1 to n (lenth of each ... A: It all depends on the function that is being looked at. For derivatives, all continuous functions ... | |
| inverse functions | 8/3/2010 |
| Q: I'm having a really hard time with this because of the square rt. Could you please help? f(x)= ... A: So when switching the x and y the problem becomes x = 3√(2y) - 3? In this case, add 3 to both ... | |
| inverse functions | 8/3/2010 |
| Q: I'm having a really hard time with this because of the square rt. Could you please help? f(x)= ... A: Is the line starting with f(x) f(x) = 3√(2x-3), what is the inverse, f^-1(x)? Let f(x) be ... | |
| Evaluating an integral | 8/3/2010 |
| Q: How would I go about evaluating this integral? A: On some problems like this, use a u substitution with u = √x. Thus, du = 1/(2√x) dx, and ... | |
| Limits | 8/2/2010 |
| Q: Can you prove these few problems I have had trouble with please? 1. If given a function f and g, ... A: 1. Lets say that g(x) = 1/x, so at x=0, this is undefined. If f(x) = -1/x, then the lim(x->0)f(x) ... | |
| Particle Motion | 8/1/2010 |
| Q: A particle is moving along the graph of cube root of x. When x=8, the y-component of its position is ... A: a) We are given that the point is moving along y = x^(1/3). The rate of x and y motion are related ... | |
| Calculus | 8/1/2010 |
| Q: A 1 X 1 square is "dissected" by three equally spaces horizontal lines and by three equally spaced ... A: Yeah, I can visulize what's being talked about. There are four new squares shaded for each square ... | |
| Calculus | 7/28/2010 |
| Q: Suppose f(x)=(2+3x)^(1/2) and suppose that the sequence {a(n)] has the following recursive ... A: If x was 34, then f(x) = 6. If x was 2/3, then f(x) = 4. Thus, I have shown that for x to large it ... | |
| summation-integration | 7/23/2010 |
| Q: sir, what is the proof that riemann summation(limit n --> infinity, sigma i=1 to n (lenth of each ... A: This is because the Riemann Sum aprroximatets the area of each retctangle as ... | |
| Calculus-Proofs | 7/23/2010 |
| Q: I am trying to prove that the limit of a function does not exist with the delta epsilon notation. ... A: If that is (lim x->0)(1/x²), then suppose the limit is A. This means that 1/x² - A < delta for x < ... | |
| Calc | 7/22/2010 |
| Q: Suppose R is the region in the plane enclosed by y=x^2 and y=4 a)Compute the perimeter P and the ... A: First, we need to note that the curves gives x² = 4 as the intersectoin points. This means x = ±2, ... | |
| Differentiability | 7/22/2010 |
| Q: I was confused by this problem; I know the function |X-1|(absolute Value) is not differentiable at ... A: I don't think they should be used, sinde the function is not differentiable at that point. It can ... | |
| calculus, related rates | 7/22/2010 |
| Q: this is the problem. water flows into a vertical cylindrical tank at 12 cu. ft. per min.; the ... A: Water flows in at 12 ft cu., but the height only increases by 6" per min. It is known that the ... | |
| calculus, related rates | 7/21/2010 |
| Q: water is flowing into a cylindrical tank at the rate of 24 cu. ft. per min. If the radius of the ... A: Since water is incoming at 24 ft³/min, divide by the surface area to get how many feet the water is ... | |
| Calculus | 7/21/2010 |
| Q: I am working on my AP Calculus summer assignment (100 questions) and I have another one that is ... A: The length of a side on the square is 1/4 of what is cut out since there are 4 equal sides. This ... | |
| Calculus problem | 7/20/2010 |
| Q: The position of particle P at time t is given by c1(t)=(t,2t-1) and the position of particle Q at ... A: After looking at the problem, it can be solved by looking at y as the independent variable and x as ... | |
| parametric equation and gradient | 7/20/2010 |
| Q: a curve is defined parametrically by the equation X=t(cubed) -6t+4 y= t-3+2/t find dy/dx A: It can be seen that dy/dt and dx/dt can be found. It is also known that these behave just like ... | |
| Calculus | 7/20/2010 |
| Q: Here's my question! What is the domain of this function: f(x)=ln(2x+12) Thanks! A: The domain is the possible x values. It is known that the domain of the ln(t) function is for all t ... | |
| statistics | 7/13/2010 |
| Q: I'm not sure if I should be using a z score for this and if I did what would x be? Could you please ... A: To have a score 1.2 standard deviations above the mean says to start with the mean, which is 50, and ... | |
| Calculus III | 7/12/2010 |
| Q: "Hi, I hope you can help me, Iam taking calculus III this summer and I am having a little trouble ... A: To find dZ/dX and dZ/dY, they are found by taking the derivative as is. The derivative of Z² is 2ZZ' ... | |
| Calculus | 7/12/2010 |
| Q: I don't understand derivative or the dy/dx thing. Can you give a brief explanation? Thanks. A: The derivative of y is y'. If y is a function of x, the derivative is dy/dx. Usually, y = f(x), so ... | |
| Calculus | 7/11/2010 |
| Q: Find the indicated quantity for y = f(x) = 5 - x2... A) f(2) - f(1) / 2-1 B) f(1+h) - f(1) / h A: Find f(2) and f(1). Now if y = f(x) = 5 - x², then f(1) = 5 - 1² = 5 - 1 = 4 and f(2) = 5 - 2² = 5 - ... | |
| pre-calulus | 7/10/2010 |
| Q: find all the real solutions, if any,of each equation 4x-5/3-7x=4 A: The only one to be worried about were is 3=7x, for then the denominator would be 0. Multiply both ... | |
| Related Rates | 7/9/2010 |
| Q: Water is leaking out of an inverted conical tank at a rate of 12500 cm3/min at the same time that ... A: The tank has a 6m diameter at the top that is 4m. The wates is rising at 20 cm/min. The water is ... | |
| Pure Algebra | 7/9/2010 |
| Q: I am trying to write a formal proof of a rule of exponents. (ab)^n=a^n*b^n. It just seems so ... A: (ab)^n = ab*ab*ab* ... ab*ab with n replicas of a and n replicas of b. Do to the associative law of ... | |
| Rate of Change | 7/9/2010 |
| Q: A paint store sells 270 cans of paint per month at a price of $32 each. A customer survey indicates ... A: a) N = 270 + 6(x/1.2), where N is the number sold and x is the decrease in price. b) The revenue ... | |
| antiderivatives | 7/8/2010 |
| Q: I need to find the derivative for the function ƒ(x) = 3x2 + 2x − 5. I keep coming up with ... A: 3(3.4)² +2(3.4) - 5 = (3(3.4) + 2)3.4 - 5 = 12.2*3.4 - 5 = 41.48 - 5 = 36.48. Since there function ... | |
| Trig Identities | 7/7/2010 |
| Q: Does Cos^2 theta equal 2Cos theta? A: No, but cos²Θ + sin²Θ = 1 and cos(2Θ) = 2(cos²(Θ)-1). Trivia on the side: ... | |
| antiderivatives | 7/7/2010 |
| Q: I need to find the derivative for the function ƒ(x) = 3x2 + 2x − 5. I keep coming up with ... A: The antiderivative is also called the integral, but they don't say that at first. So in a week or so ... | |
| Scaling a rectangle away from a fixed point | 7/6/2010 |
| Q: I have a problem which I believe falls into the realm of calculus, but I'm no expert (that's why I'm ... A: For the big rectangle, I will put it in x-y coordinates and for the smaller rectangle, I will put it ... | |
| MA 166; Calc Two | 7/3/2010 |
| Q: Could you help with the steps to figure out cos(arctan2+arctan3) I have no idea where to start. ... A: Call the angles Θ and Ω. It is given that tanΘ=2 and tanΩ=3. On the triangle ... | |
| MA 166; Calc Two | 7/3/2010 |
| Q: According to the Beer-Lambert Law, the light intensity at a depth of x meters below the surface of ... A: a) The function is I(x) = I(0)*a^x, so the derivative is dI/dx = I(0)*ln(a)a^x since I(0) is a ... | |
| CALCULUS | 7/2/2010 |
| Q: my question is "if f is a continous function on [a,b] s.t f(a)=f(b) then there exists x,y in ]a,b[ ... A: If f is a straight line, that is true for any x and y in ]a,b[. If f is not a line, it is a curve, ... | |
| derivatives | 7/1/2010 |
| Q: I have this problem and I've found the first derivative: f(x)= x^3/3-x f'(x)=(1/3x)(3x-1) x= +-1 I ... A: I'm not sure where f'(x) = (1/3x)(3x-1) came from, but it can be rewritten as (3x-1)/(3x). If the ... | |
| Question | 6/29/2010 |
| Q: Use Trapizoid Rules to estimate Integral of 0 to 1 of 551x^550 dx. Find the value of n such that ... A: It should be noted that the value of the integral is x^551 evaluated from 1 downto 0, and that this ... | |
| Differential Calculus | 6/21/2010 |
| Q: A right circular cylinder is inscribed in a sphere of radius 10cm. If the base of the cylinder has a ... A: I'm not sure what "its value" is, for it could be the area or volume. This said, I will find each ... | |
| HELP!!!! | 6/21/2010 |
| Q: I'm working on a calculus final that must be finished tonight, can you help me?!?! Find the area ... A: Well, I only view my computer questions in the morning, so this might be a little late. The area ... | |
| calculus | 6/20/2010 |
| Q: Hey i was wonder how you find the derivative of square root x+1 by using the f(x+h)-f(x)/h A: If would be found by actually carrying out the function. That is, [√(x+h+1) - √(x+h)]/h. ... | |
| Differentiation | 6/17/2010 |
| Q: I was wondering if maybe you could help me with 2 questions in regards to derivatives. a) g(x) = ... A: a) This is a product rule between f(x) and h(x) where f(x) = (x²-1)^(1/2) and h(x) = sec^-1(x). ... | |
| Calculus - Related Rates | 6/17/2010 |
| Q: A baseball diamond is a square with side 90ft. A batter hits the ball and runs towards first base ... A: When a diamond is drawn (a tipped square), put the man at x units from home at spot A, so the ... | |
| Differentials | 6/14/2010 |
| Q: So in high school there was no clear definition of differentials but it has been implied to me ... A: I put what was given in the search box. I found http://en.wikipedia.org/wiki/Differential, but not ... | |
| Differentials | 6/14/2010 |
| Q: So in high school there was no clear definition of differentials but it has been implied to me ... A: The term 'dx' is found in calculus, and most high school teachers didn't even take calculus. If they ... | |
| algebra | 6/10/2010 |
| Q: If i were to throw a football from a height of 5 feet off the ground at a velocity of 45 ... A: The equation is -gt²/2 + vt + d, where g is gravity, v is initial velocity, and d is the original ... | |
| Calculus | 6/6/2010 |
| Q: Find the equation of the tangent line to the curve y=e^(-x) at x=-1. Find the equation of the ... A: Euler's numbers are all 0 when n is odd and something else when n is even. They can be seen here: ... | |
| Calculus | 6/4/2010 |
| Q: Find the value of k that gives f(x)=x^2-kx+2 a local minimum value of 1. A: To find the local minimum, take the derivative, giving f'(x)= 2x - k. Seting this to 0 means that x ... | |
| Calculus: Counting | 6/1/2010 |
| Q: How many ways are there to place two identical qeens on an 8 x 8 chessboard so that the queens are ... A: The following has lots of words, for that is what it took to explain. I've heard a picture is worth ... | |
| inverse of function | 5/25/2010 |
| Q: Find a formula for the inverse of the function: f(x) = sqrt((x^2)+7x) where x>0 f-1(x) = ??? A: The best way to do this is to replace f(x) with y, and then solve for x. That is, y = ... | |
| General Power Rule | 5/24/2010 |
| Q: I have a problem that I cannot seem to solve. Can you please help me to understand it? The problem ... A: Take each of the cubes and solve. Note that y³ = 9x² + 4. Now 1³ = 1, and since x² is always ... | |
| related rates | 5/17/2010 |
| Q: A balloon, leaving the ground 60 ft. from an observer, rises vertically at the rate of 10 ft per ... A: The base of the triangle involves where the baloon lifted off from and where the observer was ... | |
| calculus | 5/15/2010 |
| Q: The height of the cone is 7.7 cm and the radius is 5.2 cm. As scoops of water were added (1 scoop = ... A: It looks more like it is a cone at the bottom and a cylinder at the top, for it fills 0.5 cm for ... | |
| pwer series representation | 5/15/2010 |
| Q: let P5(x) be the quintic Maclaurin polynomial for the function f defined by x ... A: The Maclaurin polynomial is a special case of the Taylor polynomial about 0. I assume the quintic ... | |
| limit of an integral function | 5/13/2010 |
| Q: .. I just need some help regarding this question.. also please mention some basic theorems ... A: It is better to put it on one line, since it looks like lim x^2 cos(t)^2 dt ( ... | |
| limits | 5/13/2010 |
| Q: how do you find the lim as x approaches 0 of (sin5x/3x)? Thanks, Michelle A: It is known that lim(x->0) (sinx/x) = 1. Since we have sin(5x), we need a 5x on the bottom. The ... | |
| second derivative | 5/11/2010 |
| Q: what is the second derivative of f(x)=x^4 + 5x^3? please show you work thanks A: The derivative of any power of x such as f(x) = cx^n is f'(x) = cnx^(n-1) for n not 0. Thus, x^4 ... | |
| derivatives | 5/9/2010 |
| Q: "suppose that water is being emptied from a spherical tank of radius 10. if the depth of the water ... A: Let the bottom of the tank be at h=0, so the depth from the bottom is h. This makes the distance to ... | |
| Calculus - Limits | 5/6/2010 |
| Q: Hey, im in my last year of high school, but im doing Uni Maths (basic, id guess), and i dont quite ... A: A proof of a formula on limits based on the epsilon-delta definition. Here, the function is looked ... | |
| Calculus - Limits | 5/6/2010 |
| Q: Hey, im in my last year of high school, but im doing Uni Maths (basic, id guess), and i dont quite ... A: Here, f(x) is really two functions. For x>=0, f(x) = x(1+x) = x + x². FOr x<=0, f(x) = x(1-x) = x - ... | |
| Volumes of Revolution | 5/5/2010 |
| Q: As shown in the accompanying figure, a cocktail glass with a bowl shaped like a hemisphere of ... A: The cherry has diameter 2, so the radius is 1. To talk about the cherry, for a sphere, the total ... | |
| calculus help | 5/4/2010 |
| Q: Could you tell me if my answers to these questions are correct or if they are not correct maybe give ... A: 1. If y² = (3x+1)³/9x + 2, that it is y² = f/g. Taking the derivative of both sides gives 2yy' = ... | |
| double integral help | 5/4/2010 |
| Q: Use polar coordinates to calculate ∫∫R 1/((x^2 +y^2)^1/2)dA where R is the region inside ... A: This is converted to polar coordinates by the function ∫∫ f(x,y) dx dy = ∫∫ ... | |
| limit at infinity with radical | 4/30/2010 |
| Q: find the limit as x approaches infinity of: sqrt(x^2+9))/sqrt(9x^2+1) I know the answer is 1/3, but ... A: Since we ave √(x²+9)/√(9x²+1), that is the same as √[(x²+9)/(9x²+1)]. If we ... | |
| . | 4/26/2010 |
| Q: I was trying to resolve this. Can you please help me. (m-1)x + y = m mx + my = 4 A: Take the two equations as mx - x + y = m and mx + my = 4. From the 2nd equation, we can see that my ... | |
| Applied Optimization | 4/24/2010 |
| Q: well i got some struggles doing this problem. It's about Max and Min.. Find the Point P on the ... A: The distance² from (x,y) to (3,0) is (x-3)² + y². That is, D² = (x-3)² + y². If we went to minimize ... | |
| Evaluation of limit | 4/23/2010 |
| Q: Sir,I'm totally exhausted after trying to find an answer to this Q in vain.the Q is Lt-->0 ... A: So is that lim(x->0) [16(1-cos{cos(10x)})/x^4]? It is known that the lim(x->0)(10x) = 10*0 = 0. ... | |
| help! :) | 4/22/2010 |
| Q: how would you solve cosx+sinxtanx=2? A: As a 1st step, note that tanx = sinx / cosx. This makes the equation into cosx + sin²x/cosx = 2. ... | |
| calculus | 4/21/2010 |
| Q: calculate dy/dx when (xy)^3 + y = 3x A: The derivative of (xy)³ is 3(xy)² d(xy)/dx. The derivative of xy is a product rule, so it is y + ... | |
| calculus | 4/21/2010 |
| Q: 1. Find the derivative with respect to x of y = (3x + x^2)^5 2. what is dy/dx if y = (x^2 + ... A: 1. Use the chain rule. The problem is y = f^5(x), and the derivative is dy/dx = (dy/df)(df/dx). That ... | |
| tough limit with radical | 4/20/2010 |
| Q: I am generally pretty good with evaluating and simplyfying expressions, but this one is a stumper: ... A: There is another approach to try. We have (√(8-x) - 2)/(√13-x) - 3) as x approaches 4. ... | |
| Calculus optimization | 4/20/2010 |
| Q: Find the dimensions of a right circular cone with surface area 1 and maximal volume. Answers in ... A: The surface area of a cone involves the top, the bottom, and the side. The top and bottom are ... | |
| optimization/ max & min | 4/19/2010 |
| Q: Cowboy Curtis wants to build a dirt road from his ranch to the highway so that he can drive to the ... A: Take the road as entering the highway 9-x units from town. This means that the length of the road ... | |
| optimization/ max & min. | 4/19/2010 |
| Q: You are planning to make an "open-top" rectangular box from an 8" x 15" piece of cardboard by ... A: The height of the box will be x. This means that the base will be (8-2x)(15-2x) since a piece must ... | |
| Calculus (Integration) | 4/18/2010 |
| Q: I need to find the integral of 3x+4/(x^2+4)(3-x). Any help would be greatly appreciated, thanks. A: I need to find the integral of 3x+4/(x^2+4)(3-x). Any help would be greatly appreciated, thanks. ... | |
| answer this please | 4/15/2010 |
| Q: 1. Find the area of the region bounded by the curve y2 = x and the line x - 4=0 2. fin the volume of ... A: 1. ∫y²dy from 2 downto -2. Note ∫y^n dy = y^(n+1) / (n+1). 2. The integral will be ... | |
| Math equations | 4/14/2010 |
| Q: Write an equation for the line that has a slope of -3 and passes through point (2,5). A: The point-slope formula for a line is y - y0 = m(x - x0) where m is the slope and (x0,y0) is the ... | |
| Optimization | 4/12/2010 |
| Q: If 40 passengers hire a special car on a train, they will be charged 8 dollars each, but this fare ... A: If 40 passengers is $8 each and 50 passengers are $7 each, that appears that each passengerover cuts ... | |
| Calculus | 4/11/2010 |
| Q: Can you please help me with the followingWhich spring requires more material to make: A spring of ... A: The lengthof each spring, when laid out straight, is a hypoteneuse on a triangle. The 1st has r = 5 ... | |
| Calculus Related Rates | 4/10/2010 |
| Q: You have two flights A(Minneapolis to New Orleans) and B(Los Angeles to New York). The flight paths ... A: Take the city as the origin on a graph. Take north-south as the y axis and east-west as the x-axis. ... | |
| Calculus | 4/9/2010 |
| Q: Triangle abc is an equilateral triangle with side length 4 feet. Determine the dimensions of the ... A: Put the center of the bottom of this triangle on the origin with one side on the x-axis. The means ... | |
| calculus | 4/9/2010 |
| Q: What is calculus used for? A: Calculus is used in almost any field. It is used in history in simple things like calculating the ... | |
| Parabola | 4/8/2010 |
| Q: Find the vertex of the parabola y=-3x(squared)-18x+5. *I don't know how to sqaure the -3x so I put ... A: For the parbola y = -3x²- 18x + 5, the square is alt-253. Squareroots are alt-251. That is, hold ... | |
| Calculus | 4/7/2010 |
| Q: Suppose that c(x)=x^3-6x^2+20,000x is the cost of manufacturing x items. Find a production level ... A: To do this, find c'(x) and set it equal to 0. Note that c'(x) will be a parabola, and to solve it ... | |
| Calculus | 4/6/2010 |
| Q: How would you go about sketching a cubic graph, such as x^3 + y^3 + 3xy = 1? I think you need to use ... A: Let y = 1-x and put this in the equation. We have x³ + (1-x)³ + 3x(1-x). That works out to x³ + ... | |
| help | 4/6/2010 |
| Q: f(x) = X^2/4-x^2 a)find the first and second derivative b)determine the values for where the ... A: Is this f(x) = x²/(4-x²)? Add and subtract 4 from the top first, giving f(x) = (4-4+x²)/(4-x²). Note ... | |
| limits | 4/5/2010 |
| Q: part (a); calulate limit (1/x-2)^1/x-3 x->3^+ part(b) caclulate limit (1 +3/x)^2x ... A: (a) Note that A^B is the same as e^(B*ln(A)). Lets take A as 1/(x-2) and B as 1/(x-3). This makes ... | |
| Calculus II | 4/4/2010 |
| Q: I will post the entire question and then explain my dilemma. Suppose that f, g are positive ... A: Take them one at a time and determine where they go. Note that ln(x) < x^n < n^x < x^x for some ... | |
| Integration Problem | 4/3/2010 |
| Q: Int (1/(1+((x^2)-1)^(1/2)) Between limits of 1 and sqrt2. Thank you. A: The first thing to do is simplify (1/(1+((x^2)-1)^(1/2)). The denominator is 1 + 1/x², which becomes ... | |
| precal trigonometry | 4/1/2010 |
| Q: if tanxcosx=.5, what is the value of sinx?? A: Label a triangle c for the hypoteneuse, a for the far side to the angle, and b for the near side ... | |
| calculus-optimization | 3/31/2010 |
| Q: Painters are painting the second floor exterior wall of a building that adjoins a busy sidewalk. a ... A: Let the amount on the floor from the corridor be x and the amount above the corridor be y. This ... | |
| testing for convergence/divergence | 3/29/2010 |
| Q: I need to test the following for convergence/divergence for Sum n=3 to infinity: (n+1)/(n^3*ln(n+2)) ... A: I would divide the fraction into two pieces. That is, make it into n/(n^3*ln(n+2)) + ... | |
| calculus | 3/28/2010 |
| Q: find the length and width of a rectangle that has the area of 64 square feet and a minium perimeter? ... A: The perimeter is given by P = 2W + 2L, where W is the width, and L is the length. The area is given ... | |
| calculus | 3/27/2010 |
| Q: .I have several questions,hope you can help me out.. 1)If the number 120 is divided into two parts ... A: 1) Let 120-A be one part of P; the other part is then A. It says that P(A) = (120-A)A² is to be ... | |
| Real Analysis | 3/26/2010 |
| Q: What is Grouping? What is Arrangement? What is difference between Grouping and Arrangement?? Give ... A: Grouping is when terms are grouped together by some category. Arrangement is when the are arranged ... | |
| Related Rates | 3/24/2010 |
| Q: A t=0 a particle starts at the origin with a velocity of 6 feet per second and moves along the ... A: Velocity is the integral of acceleration, so if acceleration is 12t², velocity is 4t³. There is ... | |
| Calculus: Applications to Marginality | 3/23/2010 |
| Q: When production is 2000, marginal revenue is 7.5 dollars per unit and marginal cost is 8 dollars per ... A: a) This means that the amount spent ($8) is more than the amount earned ($7.50), so the maximum ... | |
| Please help | 3/22/2010 |
| Q: 1. Determine the quadratic equation for the parabola: maximum value: 6; x-intercepts: -2 and 4 ... A: 1. Intercepts at -2 and 4 imply that it is y=C(x+2)(x-4) => y = C(x²-2x-8) where C is a constant. ... | |
| epsilon-delta | 3/22/2010 |
| Q: Using the formal definition of epsilon-delta definition of a limit, prove that lim[x->2]x^2=4. A: Let d be delta and e be epsilon. Then let f be the next small variable. Lets suppse the |x²-4|<e, ... | |
| General derivatives | 3/21/2010 |
| Q: General derivatives If f(x)=x^2 +sinx, find d/dx[f(5x)] and also...... If f(x)=2x+3, find ... A: The way to do this problem is with the chain rule. Note that f(5x) = (5x)² + sin(5x) = 25x² + ... | |
| Derivative of logarithm or exponential | 3/21/2010 |
| Q: Derivative of logarithm or exponential If y= 1/2ln(x^2+5), then dy/dx= A: If that y = 1/(2ln(x²+5)) or = (1/2)ln(x²+5), which can be rewritten as ln(x²+5) / 2? If it is y = ... | |
| Please help! I am so confused. :( | 3/20/2010 |
| Q: 1.Find the maximum value of the function: y = -x^2 + 8x - 4 A)8 B)22 C)16 D)12 Determine ... A: 1.Find the maximum value of the function y = -x² + 8x - 4. The maximum can be found by taking the ... | |
| parametic equations | 3/19/2010 |
| Q: Ok, I have this problem on my homework and I'm really stumped about it. Consider the parametric ... A: Yes, there are correct. To graph it, take a sheet of graph paper and count each space as a tenth. ... | |
| normal and tangent lines | 3/18/2010 |
| Q: What is the slope of the line tangent to the curve y = arctan (4x) when x = ¼ ? A: Ii can be done it by 4x = tan(y). Taking the derivative gives 4 dx = sec²y dy. Thig can be solved ... | |
| max/min problems | 3/18/2010 |
| Q: A store csn sell 500 pens, which cost the store 35 cents each, for $1 each. For each penny the store ... A: What to note is that since theyare sold for $1 and cost 35c, the profit is 65c each. The equation ... | |
| Calculus question | 3/17/2010 |
| Q: Can you please help with this.... Find the radius of convergence R for the sum from 1 to infinity ... A: If x^n is left out, then n^n/n! is the same as (n/1)(n/2)...(n/n) goes to infinity as n goes to ... | |
| Physics | 3/17/2010 |
| Q: hey so i was wondering if you knew anything about physics, i cant get onto my usual tutoring site ... A: I know a lot about physics. There are many equations I can use. They deal with speed of a ... | |
| Precalculus | 3/16/2010 |
| Q: Write the equation of the circle that is tangent to the y-axis at (0,3) and contains the point ... A: Tangent to the y axis means the edge of the circle barely touches the y axis at (0,3). The equation ... | |
| Calculus | 3/15/2010 |
| Q: I have 2 calculus problems regarding deravatives and max min (optimization). Any help is ... A: 1. The number of apples is N = (1000-20M) where M=months. The price is P = 2.50 + 1.25M. The amount ... | |
| Calculus | 3/14/2010 |
| Q: Scotto. As you have helped me greatly in the past, I would like to thank you for that. I had another ... A: We have x going from 0 to 9 and the function as √x. The area of each rectangle is 2√x * ... | |
| differentiation maxima and minima | 3/13/2010 |
| Q: i understand that when a function reaches a maximum value when it stops increasing and starts ... A: The line segment is y = -3x/2 + 3. Since P = 3x² + 2y² and the equation is on the line y = -3x/2 + ... | |
| Newton-Raphson method | 3/12/2010 |
| Q: I have this problem in Newton Raphson method and would like your help on how to solve it so as to ... A: The Newton-Raphson method is x(n+1) = xn - a(xn)/a'(xn) where xn is on term in the series and x(n+1) ... | |
| Application of Derivatives | 3/12/2010 |
| Q: At 9am ship A is 50km east of ship B. Ship A is sailing north at 40km/h and ship B is sailing south ... A: It makes no difference how far A is from B when we are given how fast they are travelling. As long ... | |
| cal II | 3/10/2010 |
| Q: i've some problems to solve this integral x^3sqrt(4 -x^2)dx i should solve it using trigonometric ... A: Now gives the equation is ∫2sin³Θ*cos²Θ dΘ, make sin²(Θ) into 1 - ... | |
| related rates | 3/9/2010 |
| Q: I can do other related rates volume problems but im having trouble with boxes for some reason A ... A: The surface area is 25x20 = 500. Since this is rising at only 0.025 feet/minute, that is 0.025*500 = ... | |
| Double integral | 3/8/2010 |
| Q: In our university mathematics course,I saw that the double integral could give both area and ... A: Most of the time a double integral is for the area and a triple integral is for volume, but ... | |
| calculus help | 3/8/2010 |
| Q: A rocket rises vertically from a point on the ground that is 100 m from an observer at ground level. ... A: The x measurement is 100. The y measurement is unknown. From both of these, it is known that r² = ... | |
| limits question | 3/7/2010 |
| Q: I'm stuck on these two questions: Evaluate (1-lnx)/e^(1/x) as x→0+ and (1/x - 1/((e^x) - 1)) ... A: As x->0, ln(x)->-infinity,so 1-ln(x)->infinity. As x->0, 1/x->infinity, so e^(1/x)->e^infinity, ... | |
| calculus help | 3/7/2010 |
| Q: A rocket rises vertically from a point on the ground that is 100 m from an observer at ground level. ... A: Convert to polar coordinates. Use x² + y² = r² and y/x = tanΘ., where x is a constant of 100. ... | |
| Calculus rate problem | 3/6/2010 |
| Q: A 50 foot tree falls such that the angle with the ground is decreasing at 5 degrees per second.(a) ... A: Convert the problem to polar coordinates. That means y/x = tanΘ and r² = x² + y². Take the ... | |
| Differentiation | 3/6/2010 |
| Q: I am trying to find dV/dp for the folowing equation: (p+(n^2a/V^2))(V-nb)=nRT I know it is an ... A: I take the dervative as is. Note that it is a product rule between f(p) = (p+(n^2a/V^2)) and g(p) = ... | |
| Calculus: Work and Force. | 3/5/2010 |
| Q: Find the work required to project a 7 oz object initially at rest to 150ft/sec. The answer needs to ... A: 7 oz, 150'/s W=m(v2²-v1²)/2 where W is the work, m is the mass, v2 is the ending velocty and v2 is ... | |
| Calculus 2 - Work | 3/2/2010 |
| Q: The top of a cylindrical storage tank for gasoline (weight of gas = 42 lbs/ ft^3) at a service ... A: The tank is 4' below ground and it is going to 3 feet above ground, so the integral starts at 7. ... | |
| The Fundamental Theorem of Calculus | 3/1/2010 |
| Q: Evaluate the integral by interpreting it as area and using formulas from geometry. (integral from ... A: The problem is really ∫∫ 1 dy dx, where y goes from 0 to √(64-x²) and x goes from ... | |
| absolute value | 2/28/2010 |
| Q: Greetings Sir, Just wondering if there is a nice polynomial formula for absolute values.i.e formula ... A: The polynomial equation is really two piecewise linear equations. That is, |x|: f(x) = x for x>0 ... | |
| calculus problem on derivatives | 2/28/2010 |
| Q: The frequency of the note produced by a guitar string is interpreted by the ear as pitch, and the ... A: In this problem, all of the values are measurements, which means they are all positive. If the ... | |
| Pool Volume | 2/27/2010 |
| Q: Consider the region bounded by f(x)=sin(pi x) and g(x)=x^3-4x. The given region is the surface of a ... A: The curves f(x) and g(x) intersect at -2, 0, and 2. Since we are talking about x as a measurement, ... | |
| derivative of a function | 2/27/2010 |
| Q: find the derivative of the following part(a): y= sqrt(x^4 + 1)tan2x part(b): f(x)= sqrt(3x/x^2+4) ... A: Find the derivatives: y = √(x^4 + 1)*tan(2x) Product rule with f(x)= √(x^4 + 1) and ... | |
| limit | 2/26/2010 |
| Q: ple tell me method how to find the limit of trigometri function A: If you're looking for the limit as x goes to infinity of a trig function, there is not one since the ... | |
| Functions. | 2/25/2010 |
| Q: just a quick question. What would be the domain of the function f(x) = (x-2)/(x^3+x) ? A: The only way a point can't be in the domain is if the function is trying to find the squareroot of a ... | |
| Infinite Series | 2/23/2010 |
| Q: How would I find whether the summation of arctan(k)/(1+k^2) from 1 to infinity diverges or ... A: It is known that the summation of 1/k² converges. Each term in the summation of 1/(1+k²) is less ... | |
| cal 2 | 2/22/2010 |
| Q: i've some questions regarding cal 2 how can integrate the following? 1- e^(x^2)*x^3 dx 2- ... A: 1. Integration by parts. Let u = x² and dv = x(e^x²). This gives u = 2x and dv = e^x²/2. 2. ... | |
| Calculus | 2/20/2010 |
| Q: I had a question about solving for the area between curves. If f(x) = x^3-3x+3 and g(x) = 2x+1. I ... A: To find the area 1) set the equations equal 2) move all of elements to one side by subtracting off ... | |
| calculus | 2/19/2010 |
| Q: An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of ... A: The airplane is 5 miles straight up. The speed of the airplane is 600 m/h. A little later on, the ... | |
| calculus | 2/19/2010 |
| Q: the point on the curve x^2 + 2y=0 that is nearest the point (0,-1/2) occurs where y is? A: The curve can be rewritten (or is it re-typed?) as y = -x²/2. Take a point on it. It can be said ... | |
| calculus | 2/17/2010 |
| Q: can u pls help me solve this problem? (3x^-3y^2z^-1/2x^-2y^-1z)^-2 root24x^-6y^3z^2/6x^-2yz^-4 A: The equation is, as I see it, ... | |
| Calculus II | 2/15/2010 |
| Q: What is the volume of the solid obtained? A region R is bounded by y=0, y=f(x)>0, x=o, x=t>0. If R ... A: To find the volumne when rotated about the x-axis, that would be ∫πf²(x)dx from 0 to t. ... | |
| Advanced Calculus of One Variable | 2/10/2010 |
| Q: Disprove the conjecture Conjecture: If {|a_n|}_n converges to |A|, then {a_n}_n converges to A A: Not so. A could be positive. Let a_n be -1 + 1/n where n goes to infinity. The |a_n| converges to ... | |
| I need help with a derivative | 2/10/2010 |
| Q: i need to find y'(1) for the following y = x^3/2 + 2 ___________ x A: We have y = f(x)/g(x). I will assume that x^3/2 is really suppose to be √x³ and not x³/2. To ... | |
| Arctan integration | 2/9/2010 |
| Q: I am trying to figure out how to do a double integral that needs to be converted to polar ... A: What I do know is that y/x = tan(θ), so arctan(y/x) is θ. The value of θ varies from ... | |
| Derivatives at 0, intervals where the function is increasing/decreasing | 2/8/2010 |
| Q: h(x)= (25x^2+15x-9)(5x+3)^2 I need to find the derivative of the function and simplify the result ... A: The function is h(x) = (25x² + 15x - 9)(25x² + 30x+ 9). The derivative would be found by the product ... | |
| Related Rates | 2/8/2010 |
| Q: I'm having some difficulty with solving this problem, I'm not even sure where to start on it. Each ... A: For a square to have an area of 16cm², each side must be √(16cm²) = 4 cm. The formula for the ... | |
| calculus | 2/7/2010 |
| Q: lim x->1 (x^4-1)/(x^3-1) A: Numerator Note that x^4 - 1 is a difference of x^2 squared minus 1 squared. This makes if factor ... | |
| Calculus | 2/6/2010 |
| Q: Hey, sorry for your time. This is the Q sir, Find the X-coordinate of the point of the curve ... A: To sketch and graph it, do it on Excel. As far as doing it mathemtically, we are given that y = ... | |
| Functions and their graphs | 2/6/2010 |
| Q: Define f(x) to be the larger of x and 2-x. Sketch the graph f(x). What are its domain and range? ... A: The graph will be in the form of a V with 45° slopes that has a vertex at (2,0). The domain is all x ... | |
| Differential calculus: Optimization | 2/5/2010 |
| Q: Can you please help me with this problems? 1. A rectangular building will be constructed on a lot in ... A: 1. The lot is 60 by 80, so the diagonal has length L = √(60²+80²) = √(3600+6400) = ... | |
| Stationary points | 2/4/2010 |
| Q: I am having trouble identifying the i) stationary points, and ii) the nature of the stationary ... A: A stationary point will be where the slope is 0. It can be seen that df/dx = 6x + 6y + 12 and df/dy ... | |
| Calc. HELP!!!! | 2/4/2010 |
| Q: 1.given y=x^2-2x+3 find the equation for the line which contains (2,3) and is perpendicular to the ... A: 1. If the slope of a line is m, the perpendicular slope is -1/m. The slope of a tangent has the ... | |
| Calculus | 2/3/2010 |
| Q: Assume the number of hours of daylight in portland, Oregon is a transformed sine graph(also known as ... A: For a sine wave, the minimum is -1 and the maximum is 1, so the range is 2. For the hours of ... | |
| Conic Sections | 2/3/2010 |
| Q: Find the vertices, foci, axes and center of the conic section: 8y^2+6x^2-36x-64y-134=0 A: First, regroup the terms and factor out the square coefficient. This gives 8(y²-8y) + 6(x²-6x) = ... | |
| Area of two curves. | 2/2/2010 |
| Q: There is a line through the origin that divides the region bounded by the parabola y = 7 x - 8 x^2 ... A: The parabola, f(x) = 7x - 8x², has a maximum where f'(x) = 0, so at 7 - 16x. Setting 7 - 16x to 0 ... | |
| Confidence interval | 2/1/2010 |
| Q: A car leasing firm is interested in the average usage of fuel (in litres) per 100 km for a certain ... A: The formula for the standard deviation is (sum(xi²) - [sum(xi)]²/n)/(n-1). In this case, n=8, so ... | |
| using trig identities | 1/31/2010 |
| Q: In each case, find sin(α), cos(α), tan(α), csc(α), sec(α), and cot(α). ... A: Since the sin(2α) is -15/17 and 2α is in the III quadrant, that makes the other side ... | |
| Volume problems? | 1/30/2010 |
| Q: sorry for your time. I have three volume problems, but my issue is ALWAYS the first step: Do I use ... A: The answer is all three are used. The outer one is a dsik and the inner one is a disk. Taking the ... | |
| Calc 2 | 1/27/2010 |
| Q: The table below gives the power consumption in megawatts in San Diego Country from midnight to ... A: There are 13 points, which make 12 intervals. There is one interval from 0:00 to 1:00, another from ... | |
| Calc 2 | 1/27/2010 |
| Q: my name is Yuriy and I am having difficulties applying the Trapezoid Rule and the Simpson's Rule. ... A: The error on the trapezoidal rule is given by K(b-a)³/12n², where K >= |f"(x)| for all x in 0 to ... | |
| integrals | 1/25/2010 |
| Q: I'm having trouble with integrals, and the problem I'm stuck on is this: (pi/3 | ... A: Now are variable in the integral was really theta, but I'll change it to x, so we're doing ... | |
| Differential Equations | 1/24/2010 |
| Q: I am having problems with writing the differential equation to: "A spherical raindrop evaporates at ... A: The volume V = 4πr³/3 and the surface area is 4πr². The rate of change of volume is ... | |
| Is rationalization actually necessary? | 1/21/2010 |
| Q: My colleagues and I have been having a very animated discussion about why we still teach students to ... A: I don't know of any rule, but all mathematicians I have met like to rationalize the denominator. ... | |
| definite integral | 1/19/2010 |
| Q: Evaluate the definite integral {pi |10sin(x)dx }0 How do I do this with sin and pi involved?? ... A: The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). That means the integral ... | |
| Derivatives | 1/18/2010 |
| Q: I am working on a problem to find the derivative of f'(x) if f(x) = 3/x^2 + 2/ sqrt x and we have ... A: Step 1: If f(x) = 3/x² + 2/√x, then f(x+h) = 3/(x+h)² + 2/√(x+h). Step 2: If we take ... | |
| Marginal Amounts | 1/13/2010 |
| Q: 1. You are designing a rectangular poster to contain 256 in squared of printing with a 3 in margin ... A: 1. It is known that 16² = 256, so we need an area that is 16x16 with a border. There are 2" on ... | |
| Trig Identities | 1/10/2010 |
| Q: Prove the indentity: 1/1-SINx + 1/1+SINx = 2 SEC^2x COT^2x + SEC^2x -TAN^2 = CSC^2 Note: X ... A: 1/(1-sonx) + 1/(1+sinx) should have a common denominator. The common denominator is 1-sin²x. ... | |
| Derivative | 1/9/2010 |
| Q: Find the location of all horizontal and vertical tangents... 1)). x * y^2 - 2y = 2 2)). x^2 + ... A: 1) The equation can be solved for x. It works out to b e xy² = 2y + 2, which then goes to x = ... | |
| question about partial derivative | 1/8/2010 |
| Q: i want some help to answer these two questions please !! 1) f(x,y)= xy^2 - ln (xy+1) , at (0,1) ... A: When taking the partials with respect to one of the variables, hold the others as constants. What ... | |
| area. | 1/8/2010 |
| Q: Estimate the area under the graph f(x)=4/x from x=1 to x=6 using 5 approximating rectangles and ... A: Since there are 5 intervals, that means 6 X values, since there is always one more X values than ... | |
| AP Calculus AB | 1/7/2010 |
| Q: The indefinite integral: integral of (((x^(1/3) + 1)^4) / (x^(2/3)))dx equals A: Basically, you want ∫ [x^(1/3) + 1]^4 / [x^(2/3)] dx. Let u = x^(1/3), then du = 1/[x^(2/3)] ... | |
| reminder | 1/6/2010 |
| Q: if f(x)/(x_1)=2 ; f(x)/(x-2)=3 find the reminder of f(x)/((x-1)(x-2)) A: If the remainder when dividing by (x-1) is 2 and the remainder when dividing by (x-2) is 3, it can ... | |
| question about partial derivative | 1/6/2010 |
| Q: i want some help to answer these two questions please !! 1) f(x,y)= xy^2 - ln (xy+1) , at (0,1) ... A: 1) fx = ∂f/∂x, and that was given as y² - y/(xy+1). fy = ∂f/∂y, and that was ... | |
| question about partial derivative | 1/5/2010 |
| Q: i want some help to answer these two questions please !! 1) f(x,y)= xy^2 - ln (xy+1) , at (0,1) ... A: The partial derivative means to hold the other variable constant. 1) Treating y as a constant, it ... | |
| cal.III | 1/4/2010 |
| Q: 3 1- how can i calculate the double integral of xcos(2x+y)dA 0<= x <= 2pi/6 , 0<=y<=pi/4 that ... A: First, a not on what was given: I'm unclear how x•sin(2x+y) is equal to x•sin(2x+pi/4) - x•sin(2x). ... | |
| Logarithms | 12/22/2009 |
| Q: First of all i would like to thank u for the answer u gave me related to log. Here is another ... A: I believe the easiest way to find a solution is to use a spreadsheet and solve for x using the ... | |
| calculus derivative help :/ | 12/18/2009 |
| Q: I was wondering if you could help me with 2 derivative problems? 1. derivative of f(x) = ... A: 1. If f(x) = √(3-5•ln(x)), that is a chain rule. The chain rule states that d(f(g(x))/dx = ... | |
| Calculus | 12/15/2009 |
| Q: Find the volume of the largest right circular cone that can be inscribed in a sphere of radius r. ... A: Let the cone have a point at the top of the sphere. Let w be the distance between the center of the ... | |
| functions and identities | 12/11/2009 |
| Q: I am preparing for a placement exam to go back to school and i am in the process of working out the ... A: Since sin(x) is (length of the far side)/(length of the hypoteneuse), that means the far side has ... | |
| calculus | 12/9/2009 |
| Q: Find the average value of the function F(t) = cos(t) in the interval 0 < t <pi. A: The average value would be ∫(0 to π)cos(t) dt / π. The integeral of cos(t) is known ... | |
| Applied max/min | 12/3/2009 |
| Q: A herpetologist is designing a rectangular experimental iguana pen to fit in the 8' by 20' corner of ... A: If it were only fenced on two sides and put in the corner, it could easily take up all the room, so ... | |
| L'Hopital's rule doesnt work | 12/2/2009 |
| Q: My professor gave my class as interesting question today. He told us to go find the answer but ... A: That statement is wrong. L'hospital's rule does work. We have f(x) = g(x)/h(x). It is seen that ... | |
| Clac | 12/1/2009 |
| Q: I have many questions like this one and was wondering if you knew how to go about it? Thanks a lot. ... A: That must be the parabola y = 6 - x². So if the base is at x and one side, it is at -x on the other, ... | |
| Calculus | 11/29/2009 |
| Q: Can you help me with this question please? (This question is from the differentiation chapter of ... A: a) (f+g)'(2) = f'(2) + g'(2) = 5 - 6 = -1. b) (f x g)'1 = f'(1) x g'(1) = -4 * -2 = 8. c) ... | |
| Calc Help. | 11/29/2009 |
| Q: Let f be a differentiable function with the following properties a. f'(x)=ax^2+bx b. f'(1)=-6 and ... A: a. Given that f'(x) = ax² + bx, it is known that f(x) = ax³/3 + bx²/2 + C. b. Given that f'(1) = ... | |
| Real Analysis; use sequences show continuos | 11/25/2009 |
| Q: given a sequence {an} n=1 -> oo a function f: N->R where f(n) = an prove that every sequence of ... A: Are N and R suppose to both be the set of real numbers? To say that the function is continuous, that ... | |
| Applied Max/Min Problem | 11/24/2009 |
| Q: I have started this question but am not sure if I am doing it correctly. Your help will be greatly ... A: The problem starts off wrong. The 3 should be a 5. When multiplying by 5/2, even the y should be ... | |
| linear approximation | 11/23/2009 |
| Q: I really appreciate your help. I am having trouble with these problems and hope you can help me. I ... A: 1) This looks like y = √x, and we take x0 = 1, so x = x0 - 0.01. The derivative is y' = ... | |
| need asap help | 11/22/2009 |
| Q: Hey I can't figure these out, do we have enough info? 1)A lighthouse is located on a small island 3 ... A: 1) Lighthouse on island 3 km from point on shore. Lighthoulse makes 4 revolutions per minutes. How ... | |
| Derivatives | 11/20/2009 |
| Q: How do I determine the fourth derivative of (x^2+1)^1/2. I can get (x^2+1)for the first derivative, ... A: After looking through it, I found an error. After checking it again, it looked fine. Here is the ... | |
| Calculus | 11/19/2009 |
| Q: How do you locate the acbsolute extrema of this function in a closed interval? (Step by Step) f(x)= ... A: Is that supposed to be f(x) = 2x/(x²+1)? The derivative f'(x) = ((x²+1)2 - 2x*2x)/(x²+1)². That ... | |
| mathmetical problem | 11/18/2009 |
| Q: "sir I have a mathmetical problem in limit and continuty in calculas. so i'd be greatful to you for ... A: When x is in radiands, the answer is 1. This is because the Taylor's expansion of sin(x) = x - ... | |
| Related Rates | 11/8/2009 |
| Q: An athlete is running around a track at constant speed. The track is a rectangle of width R and ... A: The runner is running at a constant speed of K. The coach is standing at (x,y). The runner is at ... | |
| Proving L'hospital's rule | 11/8/2009 |
| Q: if f'' is continuous show that Lim h->0 f(x + h) -2f(x) + f(x-h) ------------------------ h^2 = ... A: Note that this can be rewritten. It is really (f(x+h) - f(x)) - (f(x) - f(x-h))/h². It can be ... | |
| related rates | 11/8/2009 |
| Q: A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles ... A: (a) To do this, we need to know the surface area. Since width = height, to width a the surface is ... | |
| related rates | 11/8/2009 |
| Q: For the baseball diamond shown in the figure below, suppose the player is running from first to ... A: Since the distance between each base is 90', he is 90-34=56' from 1st base. The right triangle ... | |
| Optimization Problem | 11/7/2009 |
| Q: Can you show me how to work through this problem? I have have a lot of trouble. THANKS!! A car ... A: There are 29 dollars for 210 cars rented. For each 1 increase in dollars, there are 5 fewer cars. ... | |
| Calculus | 11/6/2009 |
| Q: Let f(x)=(x^2)+4, g(x)=√(x-1) and j(x)=(g×f)(x). a) Find the average rate of change of j(x) ... A: a) It is known that j = √((x²+4)-1) = √(x²+3). The rate of change is the derivative. To ... | |
| Calculus | 11/6/2009 |
| Q: Find a point on the graph of y=e^(5x) at which the tangent line passes through the origin A: The line passing through the origin has to be of the form y = mx. The line and curve have to have ... | |
| tangent lines | 11/6/2009 |
| Q: Find the equations of both tangent lines to the ellipse (x^2/4)+(y^2/9)=1 that passes through the ... A: I think, after all these days, that I have come up with something. Line: The equation is y-0 = ... | |
| zeroes | 11/6/2009 |
| Q: I have found the derivative of this function i asked about earlier but now i can't seem to find a ... A: The derivative is the quotient rule where f(x) = g(x)/h(x) where g(x) = 2009^x and h(x) = x^2009. ... | |
| Calculate points on a curve | 11/5/2009 |
| Q: I am trying to calculate points on a curve. The length is 90.75" by 6" height. I wanted the below ... A: This picture would look a lot better if added on in a JPG file. From what I can see, we can ... | |
| Calculus #3 | 11/5/2009 |
| Q: See the attachment - I have started this and I'm stuck on where to go from what I got. Thanks! A: The length of the rod is 1200 cm. The radius of the wheel is 40 cm. Draw a ling (or picture a line) ... | |
| Calc Related Rates | 11/5/2009 |
| Q: The volume of a cube is expanding at a constant rate of 2cm^3/sec. How fast is the length of an edge ... A: The volume V(t) is equal to the side s(t) to the third. That is, V(t) = s³(t). Given this, the ... | |
| calculus | 11/5/2009 |
| Q: A particle moves along the x-axis so that its x-coordinate at time t is given by x=ae^-kt+be^kt. ... A: It is known that the derivative of e^kt = ke^kt. The acceleration is two derivatives of the ... | |
| calculus | 11/5/2009 |
| Q: A particle moves along the x-axis so that its x-coordinate at time t is given by x=ae^-kt+be^kt. ... A: We know that x(t) = ae^-kt + be^kt. From this, we can say that x'(t) = -kae^-kt + kbe^kt. Once we ... | |
| calculus | 11/4/2009 |
| Q: Find the equation of the tangent line to the curve f(x)=x^3 that is parallel to the line ... A: The equation of the line should be put in the form where the slope can be read. That is, y = mx + b, ... | |
| Slope of line tangent to curve | 11/4/2009 |
| Q: The slope of the line tangent to the curve y squared + (xy +1)cubed= 0 at (2,-1) is... A: Let x be a function on y, so x is f(y). That is, y² + (xy + 1)³ = 0. This says that (xy+1)³ = -y². ... | |
| calculus | 11/4/2009 |
| Q: the question ask, to find the point on the graph of the curve given by y^2 = 2x that is closest to ... A: My answer was modified slightly, but it was correct. If you had any trouble comprehending my 1st ... | |
| Pre-Calculus | 11/3/2009 |
| Q: I need help with this problem, please: Solve the equation 2cos x + cos x csc x = 0 , finding ... A: The equation can have a cos x factored out of it. The equation is then cos x(2 + csc x) = 0. It is ... | |
| ap calculus ab | 11/3/2009 |
| Q: my problems (set 1): In Exercises 4, 6, 10, 15, 17, 18 use the result of these problems to find ... A: 4. y = x^4/2 + 7/2, so y' = 5x^3/2 = 2x^3. 6. y = √2•x + 1/√2, so y' = √2. 10. y ... | |
| Question | 11/3/2009 |
| Q: Intelligence reports to the U.S. fleet admiral the an enemy task force is located 120 nautical miles ... A: Refer to the drawing. Note that the left 40° was given, so at the top we have another 40°. This is ... | |
| calculas | 11/2/2009 |
| Q: if f = (1+x)^1/2/(1-x)^1/2 find dy / dx A: The function is f(x) = √g(x) where g(x) (1+x)/(1-x). The derivative is g'(x)/(2√g(x)) ... | |
| particles... | 10/31/2009 |
| Q: this one of my homework problems that i am unable to figure out. i hope you can help! A particle ... A: a.) The particle moves counterclockwise around that ellipse. That means dx/dt is positive in ... | |
| Calculus | 10/31/2009 |
| Q: If x^2 + xy + y^3 = 1; find the value of y'' at the point where x = 1. A: Given the function x² + xy + y³=1, differentiate everything, and get 2x + xy' + y + 3y²y'=0. ... | |
| number sequence | 10/29/2009 |
| Q: i have been working on this number sequence all day and cant find the pattern. can you help. ... A: I found the answer,and its down below the ===============================. To show you what else was ... | |
| second derivative implicit situation | 10/29/2009 |
| Q: teacher and I started working through this problem and then started second guessing myself. ... A: Which is the same thing that I got, only the (-6xy^2 + y^4) was switched around. I have this habit ... | |
| Rate of Change | 10/29/2009 |
| Q: Our prof is giving us some questions that he has never gone over in class so I was wondering if ... A: 1. So we've got y = x²/4. That makes the position (x, x²/4). We are given dx/dt = 5cm/s. Well, the ... | |
| pre-cal | 10/28/2009 |
| Q: I would really appreciate the quick help! and explanations as well so I can understand it as much as ... A: 1. Use long division to divide x^3+7x^2+6x-18 by x+3 Take 1 3 and divide it into 1 7 6 –18 be ... | |
| mechanics | 10/28/2009 |
| Q: A quarter circle shaped thin lamina of radius r is suspended freely at one of its ... A: I bet I forgot to include the graph - you'll have to write back for it, since I can't attach it to ... | |
| Arc Length/Set Area problem | 10/28/2009 |
| Q: I have a lab due on Mathematica, and the last question is a contest. The goal is to find a ... A: Take the function sin(x). It is 0 at x=0 and at x=π. That meets (a). OK, lets take the ... | |
| Calculus - Related Rates | 10/28/2009 |
| Q: Let V be the volume and S the total surface area of a solid right circular cylinder that is 5 feet ... A: V = volume = πr²h; S = surface area = 2π(r²+h); h = 5. This means that V = 5πr² and S ... | |
| second derivative implicit situation | 10/27/2009 |
| Q: teacher and I started working through this problem and then started second guessing myself. ... A: I know you didn't care about y", but I still must correct my error. I said the denominator for y" ... | |
| AP Calculus | 10/26/2009 |
| Q: Find the critical numbers of f(if any). Find the open intervals on which the function is increasing ... A: To find the critical values, take the first derivative. That is, f'(x) = 3x² - 12x. This factors to ... | |
| equation of plane | 10/26/2009 |
| Q: find the equation of plane which passes through the point (3,4,5), has an x intercept equal to -5 ... A: If we solve both for z, that gives z = (-2x+y)/3 and z = (x+2y+3)/2. Setting these equal gives ... | |
| ap calculus ab | 10/25/2009 |
| Q: My Problems (set 1): 1. In Exercise 1, a function y=f(x) and values x0 and x1 are given. (a) Find ... A: 1. In Exercise 1, a function y=f(x) and values x0 and x1 are given. (a) Find the average rate of ... | |
| equation of plane passing through line of intersection two other planes | 10/25/2009 |
| Q: find the equation of the plane passing through the line of intersection of the planes 2x-y+3z=0 and ... A: Take the two planes defined by 2x-y+3z=0 and x+2y-2z-3=0, and take the second times 2. This gives ... | |
| Math | 10/24/2009 |
| Q: 3 ln (x + 7) - 4 ln (x^2 + 7) A: When 4•ln(3) is seen, it is the same as ln(3^4). This said, 3•ln(x+7) is the same as ln((x+7)^3). ... | |
| Car Related Rate/Optimization | 10/22/2009 |
| Q: At 9.AM, car B is 25 km west of another car A. Car A then travels to the south at 30 km/h and car B ... A: Draw an x-y graph with car A at the origin. The position of car A is -30t in the y direction. The ... | |
| indeterminate forms and improper integrals | 10/22/2009 |
| Q: i have a problem i've been working on for a while now and i just can't solve it. the problem is lim ... A: Take f(t)/g(t) as (√t - t²)/ln(t), so f(t) = √t - t² and g(t) = ln(t). Since both the ... | |
| calculus | 10/21/2009 |
| Q: a farmer has 1000 feet of fence and wants to divide his pasture into 3 adjacent pens. What ... A: I will say the lot is X x Y. Side X only has two sides, whereas side Y has the two sides plus two ... | |
| Related rates | 10/21/2009 |
| Q: At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship ... A: Take where ship B is as the origin, which puts A at –10. Ship A’s position is given by P(A) = 10 + ... | |
| quotient rule | 10/21/2009 |
| Q: find f'(x)of (10xx+2) and the whole thing square root A: If that f(x) = √(10x² + 2) ? Note that √ is the same as ^(1/2) { to the 1/2 power }. ... | |
| optimization problem | 10/21/2009 |
| Q: a botanical display is to be constructed as a rectangular region with a river on one side and ... A: One side of the building is on the river, and I'll call that L. The width of the building I'll call ... | |
| Calculus | 10/20/2009 |
| Q: Find the equation of the tangent line to the curve y=4secx–8cosx at the point (pi/3,4) I got as far ... A: Given the function y = 4 secx – 8•cosx, find the slope at (π/3,4). If we put π/3 into the ... | |
| calculus | 10/20/2009 |
| Q: Trica works in sales. She is constantly adding to her client network. At the same time, she is also ... A: 1) C = 72 + 4m and A = 2967 + 81m, where m is for number of months. Since A is the amount per ... | |
| Rate of Change | 10/20/2009 |
| Q: The area of a sector in a circle is given by the formula A = 1/2 r2(theta) where r is the radius and ... A: I will take A = r²Θ/2. (a) The rate of change of A with respect to Θ is dA/dΘ = ... | |
| Calculus | 10/20/2009 |
| Q: Find the critical numbers for f(x)=(2x-3)/(x^2-9). I know how to set the problem up but I'm having ... A: There are vertical assymptotes at 3 and -3. The derivative is ((x²-9)2 - (2x-3)2x)/(x²-9)². The ... | |
| Mathematics (Calculus) | 10/20/2009 |
| Q: I am troubled in this question. If f(x) = │x-1│-│x│ then discuss continuity ... A: Continuity --------------------- The value is continuous everywhere. The points to check to make ... | |
| Precalculus Questions | 10/19/2009 |
| Q: I have some difficult questions, could you show me how you get the answer? 1. Tashi deposits ... A: 1a) The amount is $10,000, the interest is 8% = 0.08, and the years are 25. The final amount is F = ... | |
| math | 10/19/2009 |
| Q: I just don't know where to start on these questions just some advanced questions that I didn't have ... A: 1) If |x-2|<δ, then |2x-4|<ε, ε = 0.01. Looking at |x-2| and |2x-4|, it can be seen ... | |
| Calculus Help | 10/19/2009 |
| Q: An open box of maximum volume is to be made from a standard size poster board, by cutting equal ... A: The amount cut out of each corner is x•x. There are two corners in each side, so take of 2x from ... | |
| Limits | 10/17/2009 |
| Q: I am required to Prove that the limit as 'n' goes to infinity (e^(-n))=0. I have never been good at ... A: Given any small number d, find a number N such that for all n >= N, e^(-n) < d. Take e^(-n) = d. ... | |
| Slopes & Tangents to Parametric Curves | 10/16/2009 |
| Q: Find the equations of the tangents to the given curve that pass through the point (15, 9). x = ... A: If t=1, then x = 9(1²) + 6 = 9 + 6 = 15 and y = 6(1³) + 3 = 6 + 3 = 9. The point at t=1 is (15,9). ... | |
| second derivatives | 10/16/2009 |
| Q: Find the first and second derivatives of the function. (x^2+7)^(1/2) 1st derivative: x(x^2 ... A: We have f(x) = (x²+7)^0.5. This gives f'(x) = x(x²+7)^-0.5. This is a function a(x) = x times a ... | |
| Slopes & Tangents to Parametric Curves | 10/16/2009 |
| Q: Find the equations of the tangents to the given curve that pass through the point (15, 9). x = ... A: At x = 15, take 15 = 9t² + 6, so 9 = 9t², so t = ±1. At t=1, y = 6+3 = 9, so t = 1 was taken. The ... | |
| quick question about implicit differentiation | 10/16/2009 |
| Q: Implicit differentiation. Calculate y' implicitly a.9x^2 +4y^2 -36=0 b.Find the slope of the ... A: a. To find y', we can differentiate the equation as is. It is 18x + 8yy' = 0, so y' = -8x/(8y) = ... | |
| Calculus Definition of a derivative | 10/15/2009 |
| Q: (f(x) = (3+x)/(1-3 x) Find the derivative using the definition of a derivative. I think I need to ... A: The funcion f(x) = g(x)/h(x). Note that f'(x) follows the quotient rule. That is, f'(x) = (lo d hi - ... | |
| optimization problem | 10/15/2009 |
| Q: Find the cheapest possible cost to run a power cable from a power station(on the coast) to a marine ... A: On land, the price is $11.50/ft. At sea, the price is $21.50/ft. Run a line straight to the coast. ... | |
| optimization problem | 10/15/2009 |
| Q: The demand equation for a manufacturer is p=200-3x, and the cost function is C(x)=75+80x-x^2, ... A: Since p=200-3x is the purchase cost and C is a fixed cost, and x is the number sold, the profit is ... | |
| ap calculus | 10/14/2009 |
| Q: My problems (set 3): 9. Find the slope-intercept form of the line satisfying the given condition. ... A: Set 3 9. Find the slope-intercept form of the line satisfying the given condition. The line has an ... | |
| Tangent Lines with Specified Slopes | 10/14/2009 |
| Q: I am having trouble with the followingFind an equation of the straight line having slope 1/4 that is ... A: t = √x, so y' = 1/(2√x). This means that at y' = 1/4, 1/4 = 1/(2√x), so 4 = ... | |
| Help getting h out of the denominator | 10/14/2009 |
| Q: limit[h:0,((x+h)^4-(x^4))/(h)] A: NOte that (x+h)^4 = x^4 + 4x^3h + 6x^2h^2 + 4xh^3 + h^4. When x^4 is subtracted off, the result is ... | |
| Calculus, Volumes of solids | 10/13/2009 |
| Q: I am having trouble with this Calculus 2 question about volumes of solids. Mainly I'm having ... A: Since the semicircles are perpendicular to the y-axis, lets take the line as y = 2 - 2x. We know ... | |
| Calculus | 10/13/2009 |
| Q: Trig Identities [4sin(x)cos(x)][1-2sin(squared)(x)]=sin(4x) and 1-cos(x) / 1+cos(x)= ... A: Note the 2sin(x)cos(x) = sin(2x), so 4sin(x)cos(x) = 2sin(2x). Note also that 1 - 2sin²(x) is is ... | |
| Maximum or Minimum | 10/12/2009 |
| Q: .. I have another question for you. I can't remember now If I asked you this or not ... Find the ... A: So the equation "x^4/4 (a fraction, x^4 over 4), + x^3 + 3/2x^2 (3/2 is a fraction) + y" is really ... | |
| Calculus | 10/12/2009 |
| Q: A boat is cruising around on a lake in the x-y plane. The x-component of the boats position is ... A: 1) x = 15, y = 20, so (x,y) = (15,20). 2) x = 15 + 60 + 100 = 175, y = 20 + 150 = 170, so (x,y) = ... | |
| circle formulae | 10/12/2009 |
| Q: Hey, I'm in first year calculus in university and it seems my prof expects us to know the xy formula ... A: The equation of a circle is (x-x0)² + (y-y0)² = r² where the center is at (x0,y0) and the radius is ... | |
| Pre Calculus -(Honors Advanced Math II class) -sine and cosin waves | 10/12/2009 |
| Q: Here's some background Information on theOne day we decide to go to six flags. They decide to go on ... A: The diamter d=14, so r=7. The gate has a perimeter of 72 meters and is square. Since perimeter is ... | |
| Pre Calculus -(Honors Advanced Math II class) -sine and cosin waves | 10/12/2009 |
| Q: Heres some background information- One day we decide to go to six flags. They decide to ride the ... A: A) If the roller coaster only rises and falls, the period is twice the amount of distance from 10 ... | |
| Pre Calculus -(Honors Advanced Math II class) | 10/12/2009 |
| Q: Here's some background information for the problem: One day w decide to go to six flags. They ... A: Take y = asin(bx) + d. At t=0 and t=2, the equation repeats. Since the sin() repeats every 2π, ... | |
| calculas | 10/12/2009 |
| Q: The potential energy of a spring is U = 1 2kx2, where x is the displacement of the spring from the ... A: Note that if U=1/(2kx²), it should be written on one line, since computer translate space much ... | |
| area of a regions bound by graphs | 10/9/2009 |
| Q: I just want to know if I got the correct answer for the following: Find the are of the region ... A: They would cross where x² - 1 = x, or where x² - x - 1 = 0. The solution to this equation would be ... | |
| Limit problem | 10/8/2009 |
| Q: f(x)= (x-3)^2 if x > 1 = 25 if x <1 if lim x -> a f(x) exists what is a? lim f(x) -> a+ ... A: The problem to be looked at is what is g(1). If f(1) = 25, the function is continuous. Now f(1) = ... | |
| calculas | 10/8/2009 |
| Q: find the number c that makes f(x) into: 1. a continuous function 2. a differentiable function in ... A: 1. It is known that lim(x->0)(sinx/x) is 1, so if we take that and divide by x again, it can be seen ... | |
| calculus-differentiation rules | 10/7/2009 |
| Q: Suppose that f (x) =2x^2/(5−4x)^4 . Find an equation for the tangent line to the graph of f at ... A: f'(x) = (lo d hi - hi d lo)/lo² = (((5-4x)^4)4x - 2x^2(4(5-4x)^3)(-4))/(5-4x)^8. We can factor ... | |
| Differential Equation- displacment | 10/6/2009 |
| Q: I have the displament of a damped spring system and it is described by the Differential Equation m ... A: To solve this, the equation that arises is mx² + cx + k = 0. Use the quadratic equation to find the ... | |
| Pre-Calc | 10/5/2009 |
| Q: How do you solve this? 2x+3≤5x+6<-3x+7 A: Recognize this as two equations. One of them is 2x+3 ≤ 5x+6 and the other is 5x+6 < -3x+7. ... | |
| Calculus | 10/5/2009 |
| Q: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). limit as x ... A: When calculating limits, put in x+h for x and see what happens as h goes to 0. Doing this gives ... | |
| ap calculus preparation | 10/4/2009 |
| Q: my problems (set 2): 2. Let g(x)= radical(x). Find: (a) g(5s+2) (b) g(radical(x)+2) (c) 3g(5x) (d) ... A: 2. Let g(x)= √x. Find: (a) put 5s+2 in for x; (b) put √x + 2 in for x; (c) put 5x in for ... | |
| Euler's Method | 10/2/2009 |
| Q: Scotto, Hope all is well with you. I need your help! a)Use Euler's Method with step size h = 0.1, ... A: Don't worry - I know the other people will get this as well, but it is suppose to be private if it ... | |
| Chemistry | 10/2/2009 |
| Q: (g) state and explain which one of the following ions will undergo greatest deflection under the ... A: I believe it would be the 7Li^2+ since it is among the greatest weight and has the greatest charge. ... | |
| ap calculus preparation | 10/1/2009 |
| Q: 32. For question 32, find the standard equation of the circle satisfying the given conditions. A ... A: Find the distance between the two points. That is the diameter d. It is know that d = 2r, where r ... | |
| Functions | 9/30/2009 |
| Q: p(1+5x) = 6/(2-3x). What is p(x)? A: To get the inverse, lets go with it is of the form 6/(A-Bx). We then get p(1+5x) = 6/(A - B - 5Bx). ... | |
| math | 9/29/2009 |
| Q: For every real number ε > 0, there exists a natural number n0 such that for all n > n0, |xn ... A: n0 is the first value in a series (i.e., n0, n1, n2, n3...). It could just as well have been called ... | |
| math | 9/28/2009 |
| Q: For every real number ε > 0, there exists a natural number n0 such that for all n > n0, |xn ... A: This is the definition of a limit. It states that for all x that are large enough, |xn - L| < e. ... | |
| Calculus | 9/25/2009 |
| Q: Use dot product to find the lenghts of the sides of the triangle with Vertices at positions (0,0,0), ... A: You might here this from other assistance, but the private should be, 'Yes'. Since it is a no, ... | |
| Calculus | 9/25/2009 |
| Q: Scotto, I am working on derivatives and differatials.....and I am stuck trying to solve the ... A: You'll probably get this from other people, but the Private should be 'yes'. If f(x) = 3/(6x+7), ... | |
| AP Calculus AB homework help | 9/24/2009 |
| Q: The line through the origin with slope=-1 is tangent to curve at point P. Find the x and y ... A: My computer accidentally sent that to you. What I meant to send you was a list of solutions to ... | |
| calculating limits | 9/23/2009 |
| Q: :) Could you tell me how to find the limit of absolute values? (ex) /10-x/over 10-x when x is ... A: The problem is |10-x|/(10-x). If x=10, the problem is undefined. If x > 10, then 10-x<0, so |10-x| ... | |
| Evaluate the integral with respect to a? | 9/23/2009 |
| Q: Evaluate the integral from 0 to infinity (e^-ax)(sinx)/x dx with respect to a? Thanks a Bunch! A: Just an update on the last letter. Note that as x < 1, to divide by x gives a greater value. ... | |
| Geometry | 9/22/2009 |
| Q: The square of any negative number is _______? A: To square a negative number, divide it into parts. The negative squared is a negatvie times a ... | |
| Calculus | 9/21/2009 |
| Q: vertify that the theorem applies to the indicated interval and find the value of c guaranteed by the ... A: It can be seen that since f(x) = x² + x - 1. From this, f(0) = -1 and f(5) = 29. Since the function ... | |
| Calculus 1 | 9/21/2009 |
| Q: I'm having trouble finding the limit, I got so far and just got stuck, Help would be a plus!! Thanks ... A: The lim(x->∞)(√(9x²+x) - 3x) = ? I will start off by saying that we should multiply by ... | |
| IVT | 9/15/2009 |
| Q: "at 8:00 am on saturday a man begins running up the side of a mountain to his weekend campsite. On ... A: To prove it exists and also find it. Since they both start at 8 am, imagine there are two people, ... | |
| differential equations | 9/10/2009 |
| Q: I'm in college calculus 2 and we went through solving differential equations with seperable ... A: In the first equation, dy/dx = (x+3x²)/y², when it is multiplied by y²dx, the result is y²dy = ... | |
| Calculus/Volume | 9/10/2009 |
| Q: Find the volume of the solid generated by revovling the region bounded by the graphs of y=x^2, and ... A: To find where the graphs intersect, set x² = 20x - x². This gives 2x² - 20x = 0, which factors to ... | |
| linear functions | 9/10/2009 |
| Q: how do i find the equation of the line that passes through the points (-1,4),(2,0) A: The slope if rise over run. The rise is 0-4 = -4 and the run is 2-(-1) = 3, so its -4/3. The point ... | |
| Pre-AP Calculus | 9/8/2009 |
| Q: Can you please explain how to do this? To solve an equation by finding x-intercepts, Cynthia ... A: To determine a factor, measure the distance in inches and call it x. One effect on the factor is in ... | |
| Finding the extremepoints | 9/6/2009 |
| Q: could you please help me a little with this question? Find and classify the extremepoints of this ... A: The way to find out is to put the value into the second partial derivatives of x and of y. Lets ... | |
| Intervals/increasing and decreasing | 9/3/2009 |
| Q: Please help me find the interval where f(x) - x^3+x^2-5x+2 is increasing and the interval where it ... A: I'm not sure what "1/6 dx^2 (25x^4+8x-9)" means. The term dx^2 usually refers to the 2nd derivative ... | |
| Intervals/increasing and decreasing | 9/3/2009 |
| Q: Please help me find the interval where f(x) - x^3+x^2-5x+2 is increasing and the interval where it ... A: A function is increasing where f'(x)>0 and decreasing where f'(x) < 0. Looking at f(x) = ... | |
| derivatives | 9/3/2009 |
| Q: How do I find the derivative of ln(sinx)? A: It is known that the derivative of g(x) = sinx is g'(x) = cosx. It is known that the derivative of ... | |
| physics | 8/12/2009 |
| Q: i have an expression which has a scalar quantity in left hand side is equal to dot product of two ... A: The dot product of two vectors is an integer. However, the sum of two vectors is still a vector. It ... | |
| Pre-Cal | 8/9/2009 |
| Q: Can you please answer these and show a few steps to help me understand. I have school tomorrow, and ... A: 3) f(x) = x2 + 1 4) g(x) = x − 3 + 2 5) h(x) = -|X+2| +1 6) find g -1 (x) From what I ... | |
| Calculus | 8/8/2009 |
| Q: The temperature of a star decays from the centre towards surface as, T(x,y,z)=Toe^-(x^4+y^4+z^4) ... A: At first I was wondering about this equation: Toe^-(x^4+y^4+z^4). What is Toe? And then I realized ... | |
| Exponential Regression. | 8/6/2009 |
| Q: Basically I have one question, its to assume that the graph of the exponential function, f(x)=ka^x ... A: Well, those are the values for x and f(x), so lets put them in. We get 1.5 = k(a^1) and 6 = k(a^-1). ... | |
| Calculus | 8/6/2009 |
| Q: using the Maclaurin Series expansion of e^x determine the maclaurin series expansion of x/ ... A: If the problem read "using the Maclaurin Series expansion of e^x as far as x^4, approximate x/(e^x ... | |
| calculus with applications | 8/5/2009 |
| Q: a candy box is made from a piece of cardboard that measures 13 by 8 inches. Squares of equal size ... A: The box is 13 by 8, and the squares will be have a length of a side known as x. Since for each side ... | |
| Calculus Question | 8/4/2009 |
| Q: Water is being collected from a block of ice with a square base. The water is produced because the ... A: The volume of the block is 15 in. x 20 in. x 20 in. = 6,000 in³. If the width is decreasing by 2 in ... | |
| intervals | 8/3/2009 |
| Q: Please help me with the following problem: Use calculus to find the intervals of increase and ... A: f(x)=x^2-(1/x^2); note that at x=0, the function is undefined. This means that f'(x) = 2x - (2/x³). ... | |
| Introduction to calculus | 8/2/2009 |
| Q: I am really having trouble with differentiate. Here are some questions I am having trouble with. ... A: Multiply the 1/(4x+5)^7 by (4x+5)/(4x+5). That gives (4x+5)/(4x+5)^8. Now that this has a common ... | |
| Tornadoes(again) | 7/31/2009 |
| Q: I was going to mention an interesting thought about that derived equation ... A: That's y' and y", which are dy/dV and d²y/dV² - right? By the way, π is alt-227. I do an ... | |
| I need help with this question | 7/30/2009 |
| Q: I'm helping someone at yahoo! answers with thisWater is flowing into a hemispherical bowl of radius ... A: So I see that you have it. Your welcome. I'll gladly answer any more. It is getting better today - ... | |
| I need help with this question | 7/29/2009 |
| Q: I'm helping someone at yahoo! answers with thisWater is flowing into a hemispherical bowl of radius ... A: The bowl is the bottom half of a sphere. This means the total volume V is half that of a sphere, or ... | |
| Calculs question | 7/28/2009 |
| Q: please see the attached question and help me out on this. A: It is known that the integral of cos(x) from B down to A is sin(B)-sin(A). sin(π/4) - ... | |
| Maths!!!!!!!! | 7/27/2009 |
| Q: Please I urgently need help with thesse two math questions. Differentiate: 1/3x^6(x^2-3) 5/square ... A: They are: x^6(x^2 - 3)/3, 5/√(4+x), and √(3x-1)/2. Right? x^6(x^2 - 3)/3 The first one ... | |
| Percentage Error Word Problem | 7/26/2009 |
| Q: A surveyor, standing 30 feet from the base of a building, measures the angle of elevation to the top ... A: Draw a traingle with base 30, lower angle 75°, and height x, where the side of length x goes up and ... | |
| Tornadoes(again) | 7/25/2009 |
| Q: I was going to mention an interesting thought about that derived equation ... A: I think one of the equations is (dV/dt)[{V/(2A)}{1 - H^3/(12c^3)} - 2/3] + 1/2. Again, it is very ... | |
| please help me in this question | 7/25/2009 |
| Q: given 2 separate functions of, k(x)={x^4-1 x<1 and, h(x)={x+1 x<-1 {x^3-8 x>2 ... A: By what's given we have to define h(x)/k(x) by the values of x<-1 and x>-1. For x<-1, the value of ... | |
| Tornado outbreaks | 7/24/2009 |
| Q: Why the October 26, 1963 Oklahoma(Browning Study) outbreak is so important. Recall that the whole ... A: So look for more, keep sending them in, and do more research into the weather. Also, it is helpful ... | |
| Tornadoes(again) | 7/23/2009 |
| Q: You are in Washington? U Dub? By the way, merely asking pointed questions to people associated with ... A: Spinal Meningitis When I was a nine-month-old child, my mom tells me that I was in the hospital for ... | |
| Tornadoes(again) | 7/23/2009 |
| Q: Youa sked about dV/dt[V/2A[(1-H^2)12c^2]-2/3]+1/2]? This is what i derived from ... A: Yeah, it does make me wonder about them. Is that equation have A e^(-kxt) sin(Bx)? Then k would ... | |
| Tornado outbreaks as deterministic events! | 7/23/2009 |
| Q: Upon further reflection, I should fully expound on the nature of theCan tornadoes mimic minimum ... A: I don't know of anyone since I'm in Washington where we don't see tornadoes much at all (I've never ... | |
| Tornado outbreaks as deterministic events! | 7/23/2009 |
| Q: Upon further reflection, I should fully expound on the nature of theCan tornadoes mimic minimum ... A: I would suggest finding a local weather reporter and submitting a report on data gathered on past ... | |
| Tornadoes(again) | 7/23/2009 |
| Q: Youa sked about dV/dt[V/2A[(1-H^2)12c^2]-2/3]+1/2]? This is what i derived from ... A: Can I assume that the equation is really dV/dt[{(V/2A)[(1-H^3)/(12c^3)]-2/3}+1/2], with parenthesis ... | |
| Introduction to calculus | 7/23/2009 |
| Q: I am really having trouble with differentiate. Here are some questions I am having trouble with. ... A: On 1/2x^3, is that [A] 1/(2x^3) or [B] (1/2) of x^3, which should be put as 2x^3/3? For [A], if ... | |
| Tornadoes(again) | 7/22/2009 |
| Q: I am glad that you asked that question of me! The value,A, stands for the distance between to points ... A: For the list of four points gives, 0, π/2, 2π/3, and π, is that what the critical ... | |
| linear thermal expansion coefficient | 7/22/2009 |
| Q: What exactly determines it? and why does it differ between the elements , is it e physical attribute ... A: Linear Thermal Expansion is based on the material and the change in termperature. If the ... | |
| Tornadoes(again) | 7/22/2009 |
| Q: I am glad that you asked that question of me! The value,A, stands for the distance between to points ... A: That cross-secitional area, given the radius, is πr². In a 90° relation, that would be 0.25 of ... | |
| Tornadoes(I got to keep this going!) | 7/22/2009 |
| Q: It is much more than wind and pressure, it may concern the "heart". If the cardioid is a solution to ... A: Just thought I might tell you that pi is really π (alt-227). I have a trivial question for ... | |
| Tornadoes(I got to keep this going!) | 7/21/2009 |
| Q: It is much more than wind and pressure, it may concern the "heart". If the cardioid is a solution to ... A: I find it rather fascinating the they have the mathematics that determine a tornadoes behavior. So ... | |
| Derivative for a piecewise function | 7/21/2009 |
| Q: COnsider the function f:R->R defined by: f(x)= ((1+x)/2) if x<1, 1 if x=1, ... A: Lets just ignore the fact I sent that document to you. I think I'm getting so I don't even reread ... | |
| Tornadoes(I got to keep this going!) | 7/20/2009 |
| Q: It is much more than wind and pressure, it may concern the "heart". If the cardioid is a solution to ... A: Here is a response with questions about it. Let me see if I've got it. Is the equation is ... | |
| Derivative for a piecewise function | 7/20/2009 |
| Q: COnsider the function f:R->R defined by: f(x)= ((1+x)/2) if x<1, 1 if x=1, ... A: The function f(x) = 1/2 for x < 1; f(x) = 1 at x = 1; and √x is x > 1. x<1 : f'(x) = 0 and ... | |
| 3rd Derivative | 7/20/2009 |
| Q: Function f(x) = x^4-3x^2 1st Der f ‘ (x) = 4x^3-6x 2nd Der f ” (x) =12x^2-6 3rd Der f ... A: OK, I thought it didn't matter that much to me, but now I've go to know - what is POI? Point Of ... | |
| Tornadoes as minimum values in surface area and volume | 7/20/2009 |
| Q: Allow me to extend my apologies as I am not familiar with your protocols there. Yes, I was ... A: It seems like all they have to know to determine exactly where the tornado will be is the air ... | |
| Geometry | 7/20/2009 |
| Q: Please how to solve the problem a) Trapezoid ABCD, AD is parallel to BC, angle A = angle D - ... A: The trapezoid can be divided into one triangle at each end (for a total of two triangles) and a ... | |
| 3rd Derivative | 7/20/2009 |
| Q: Function f(x) = x^4-3x^2 1st Der f ‘ (x) = 4x^3-6x 2nd Der f ” (x) =12x^2-6 3rd Der f ... A: 1) At the point where the acceleration (f"(x)) is the same as the derivative of acceleration, that ... | |
| implicit differenciation | 7/19/2009 |
| Q: Hey, I'm currently taking an AP calculus course and I've encountered some problems when it comes to ... A: When faced with problems like this one, get rid of the parenthesis first. Next, move all terms with ... | |
| Tornadoes as minimum values in surface area and volume | 7/18/2009 |
| Q: Allow me to extend my apologies as I am not familiar with your protocols there. Yes, I was ... A: It seems to me that there are even more constraints that are needed. Sone can be gotten, but some ... | |
| Tornadoes as minimum values in surface area and volume | 7/17/2009 |
| Q: Allow me to extend my apologies as I am not familiar with your protocols there. Yes, I was ... A: I'm sorry if I sounded upset at all, I'm just trying to understand the question. I am more ... | |
| Help! | 7/17/2009 |
| Q: I am having trouble with derivitives. I understand them but once I get to the point where I need to ... A: Note that log2x = lnx/ln2. If you are trying to differentiate this, the derivative is ((1+x)(d hi) ... | |
| Surds | 7/17/2009 |
| Q: Please help me to solve these problems a) 1/1+rt2 + 1/rt2+rt3 + 1/rt3+rt4 + .....99 terms. b) ... A: I can do (a) with a spreadsheet. I don't see how to do (b) or (c). On (d), the 4th root of a ... | |
| Precal - Trig. Identities | 7/16/2009 |
| Q: sinxcosx=1/4 what are the solutions for this identity? A: Try 15 degrees. I think that works and I have a proof if you want to see it. I'm not sure the ... | |
| advance math | 7/16/2009 |
| Q: Solve by completing the square. 1. x2 – 4x – 16 = 0 2.2x2 -7x +3 = 0 3.2x^2 – 12x+B 4 = 0 4.x^2+ ... A: 1. x^2 - 4x - 16 = 0 => x^2 - 4x + 4 - 4 - 16 = 0 => (x-2)^2 = 20 => x-2 = +/- 2rt(5) => x = 2 + ... | |
| Calculus | 7/15/2009 |
| Q: U.S. Population YEAR POPULATION 1930 122,800,000 1940 131,700,000 1950 150,700,000 1960 ... A: Take the 1960 population minus the 1950 population. Call this D for difference. This is the growth ... | |
| Surds | 7/15/2009 |
| Q: Can u help to solve this problems a)1/root10+root14+root15+root21 with rational denominator b)8th ... A: a) Whenever I see numbers that small, the factors automatically click in my head. I know that ... | |
| Curve Sketching | 7/15/2009 |
| Q: I have two problems. 1) f(x)=x*sqrt(7-x^2) 2) g(x)= sin(x)/1+cos(x) How would you find the domain? ... A: The domain is all of the x that can be put into the function. 1) This function has an x and a ... | |
| Differentiability | 7/15/2009 |
| Q: I'm a guy from India preparing for IIT(Indian Institute of Technology) entrance exams. I have a ... A: Let's take a look at g(x) = 2x/(1+x^2). By the quotient rule, g'(x) = ((1+x^2)2 - 2x*2x)/(1+x^2)^2 = ... | |
| calculus | 7/14/2009 |
| Q: Find the center, vertices, endpoints of the minor axis,eccentricity,and foci of the ellipse and the ... A: For a ellipse, the formula is ((x-x0)/a)^2 + ((y-y0)/b)^2 = 1. The center is at (x0,y0). The ... | |
| Adavance calculus | 7/9/2009 |
| Q: 1. Given ΔABC with <B = 60° , b = 21.5 and c = 12.4, find <C , to the nearest tenth of a ... A: 1. The law of cosines can be applied. It is a² = b² + c² - 2bc cos C, so all that has te be done is ... | |
| Tornadoes as minimum volume and surface area problems | 7/7/2009 |
| Q: In response, I might mention that when I tried to obtain an answer in which both surface area and ... A: That is correct - I mostly deal with mathematics. Math is what I know and what I use. I tried to ... | |
| Plastic Calculation | 7/3/2009 |
| Q: How can calculate kg into meter i. e. we are giving guage, size? OR what is meter of 1 Kg oply film ... A: If I understand the question, we have 1 kg of oply film. The film is 100 microns thick and 1000 mm ... | |
| Calc. or Numeric Analysis | 7/2/2009 |
| Q: How do you use L'Hospital's Rule to compute 1. Lim as x approaches pos 0 of (cos x - ... A: 1. Lim as x->+0 of (cos x - e^x)/(ln(1+x^2) L'Hospital's Rule says to take the derivative of the ... | |
| integration | 6/25/2009 |
| Q: I want to integrate the following function:∫(2x3 – 3x2 + 5x – 2)dx and ∫(5sin2θ + ... A: You can't find the derivative of integral, but only a numerical approximation. For derivatives, use ... | |
| need help on curve sketching | 6/25/2009 |
| Q: Given the following function, state the domain, all asymptotes, intercepts, relative extrema and ... A: The function is f(x) = (4 - x²)/(x² + 1). To find the derivative, use the quotient rule. That is, ... | |
| calculus | 6/25/2009 |
| Q: how to sketch graph of the function and how to determine the domain and range to this problem f(x)= ... A: First of all, the function is the function f(x) = √(9-x²)? If it is, then |x| <= 3, for if ... | |
| Probability | 6/23/2009 |
| Q: There are four independant systems that generate either a Win or Loss output.The Win % on each ... A: On the average you would get a little less than 43 wins per month. Unless they have more of an even ... | |
| calculus | 6/23/2009 |
| Q: how do go by State the quadrant in which the angle terminates(is found) and state the value of the ... A: The positive x axis is 0°, the positive y axis is 90°, the negative x axis is 270°, and the ... | |
| calculus | 6/23/2009 |
| Q: State the exact value, in simple radical form : (NO DECIMALS !!) 1. sin 225° 2. tan 3π/4 ... A: 1. The sin(225°) can be found by noticing that 225° the same as 180° + 45°. Now the sin() is ... | |
| Probability | 6/23/2009 |
| Q: There are four independant systems that generate either a Win or Loss output.The Win % on each ... A: THe win on the total of four systems, assuming they are all independent of each other and played ... | |
| Proving Identities | 6/23/2009 |
| Q: sin^2x/(1-cosx)^2= 1+cosx/1-cosx A: Take the right side and multiply the top and bottom by 1 - cosx. The result is ... | |
| Calculus | 6/21/2009 |
| Q: Which of the following is the best integration technique to use for ∫2x(x2 + 1)5 dx? A) The ... A: 1) As I look at what we are integrating, the first thing that pops into my head is to let u = x² + ... | |
| L'Hopital's Rule | 6/21/2009 |
| Q: What is a necessary condition for L'Hôpital's Rule to work? A) The function must be determinate. ... A: To state L'Hôpital's Rule, it says that if lim x->c f(x) = lim x->c g(x) = 0 or lim x->c g(x) = ... | |
| Calculus | 6/21/2009 |
| Q: If f(x) = 3x2, then F(x) = A) 6x B) x3 C) x3 + C D) 6x + C A: I understand that f(x) = 3x². Since F(x) is used for ∫f(x)dx, it can be seen that there are ... | |
| Inflection Point | 6/21/2009 |
| Q: Does f(c)= (c+2)^3 -2 have an inflection point? If so, where is it located? a) Yes, at (-2, -2) b) ... A: It is known that f"(c) = 0 at an inflection point. It can be seen that f'(c) = 3(c+2)^2. Now we ... | |
| TRIGONOMETRY | 6/20/2009 |
| Q: My name's Veronica and I'm currently having trouble answering these problems. I believe they have ... A: 1) Verify: sinΘcosΘ = x√(25 - x²)/25. Where theta is an acute angle of triangle ABC ... | |
| pre calc | 6/16/2009 |
| Q: for f(x)=x^2-3x+2; find f(x+h)-f(x)/h A: We are given that f(x)=x^2-3x+2. We need to find f(x+h)-f(x)/h. It can be seen that f(x+h) = ... | |
| Calculus | 6/16/2009 |
| Q: 1 .Imagine making a tent in the shape of a spherical cap (a sphere with lower portion sliced away by ... A: If that were a hemisphere that was desired on top, the problem would be simple. The volume of a ... | |
| integration | 6/11/2009 |
| Q: I want to integrate the following function:∫(2x3 – 3x2 + 5x – 2)dx and ∫(5sin2θ + ... A: The polynomial was done OK. The trig problem was done OK. Both look OK. To see if the answers are ... | |
| calculus(calculating minima) | 6/10/2009 |
| Q: sir, if i have a discrete data of variation of z with x and y. how can i find a equation z=f(x,y). ... A: If you only have values out of the distributions, a way to approximate the derivatives is to take ... | |
| Derivative | 6/8/2009 |
| Q: I'm trying to find the derivative of y=cos(e^-3x). I have the first line: ... A: All that can be done is the terms reorderd. It is common to put constants out in front. Note that ... | |
| Derivative | 6/8/2009 |
| Q: What's the derivative of y=(4x^4+16x-15)^1/4 ? Thanks. A: Note 1/4 = 0.25, 2/4 = 0.5, 3/4 = 0.75, and 4/4 = 1. Here we have y = f^0.25(x), that is, the ... | |
| Derivative | 6/8/2009 |
| Q: How do I find the derivative y = (x+1/x+2)^2 ? Thanks! A: Let y = f²(x), f(x) = x+1/x+2. Derivatives cancel just like numbers do. To find dy/dx, we can find ... | |
| Calculus | 6/8/2009 |
| Q: I need this question answered VERY soon, thanks! Determine whether the series converges or ... A: a) The constant factor out front really doesn't matter. The only way a series would converge ... | |
| Changing the subject of a formula | 6/6/2009 |
| Q: I have a question I just cant finish. I am stuck somewhere. The first part is fine. I am asked to ... A: I'll read this much of yourI have a question I just cant finish. I am stuck somewhere. The first ... | |
| Pre-calc | 6/6/2009 |
| Q: Find all the real solutions, if any, of the following equation. 4x-5/3-7x=4 okay, i solved it and ... A: The easiest way to do that is put it back into the equation. Take x = 17/32, and put into ... | |
| word problems. | 6/4/2009 |
| Q: I couldn't figure these out for a hw awhile back, could you help provide the answers with the work ... A: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley ... | |
| Derivative and evaluate | 6/3/2009 |
| Q: find the derivative and evaluate f(x)= (1+sin(x))/(tan(x)) at X=pi/6 A: Before taking the derivative, it is best to simplify the expression first and therby drop any ... | |
| volume/surface area | 6/2/2009 |
| Q: If 1200 cm cubed of material is available to make a box with a square base and and open top, find ... A: a. The base has width x, so the bottom area is x². Multiply this by the height to get the volume. ... | |
| Volume | 6/1/2009 |
| Q: I'm having some trouble with this: "Let R be the region bounded by y=x, y=0, and x=2. Find the ... A: "Let R be the region bounded by y=x, y=0, and x=2. Find the volume of the solid formed by revolving ... | |
| ln derivatives. | 5/28/2009 |
| Q: How do I do this with the abs value in it? [lnx]^2 I have to find f'(x). Thanks. !*!*!*!*!*! ... A: When ln(x) is squared, a continuous function is gotten that is always positive. The absolute value ... | |
| Derivative | 5/19/2009 |
| Q: what is the procedure to find dy/dx from this ecuation: x=y ln xy Thanks. A: Implicit differentiation is the only way that I see. The right side is a produc rule, the second ... | |
| Problem to solve | 5/18/2009 |
| Q: ) I dont know how to calculate the following: To calculate how many revolutions a tape has to go ... A: One revolution is 2πr, and in this case r starts out as 4. That means the first revolution is ... | |
| l'hospitals rule | 5/18/2009 |
| Q: i know you've said i you dont get this, but i think that you can, because you have done such a good ... A: Well, when you first asked me, I didn't think I had a clue. Now that you have asked me again, it ... | |
| Integrals | 5/17/2009 |
| Q: Compute each integral: 1) ∫b=4 a=1 √(1+√(x))dx and 2) ... A: They can be done, though they took me awhile to do. Over a half dozen pages later, I got this. 1. ... | |
| Calculus | 5/16/2009 |
| Q: i need help with problem please, thank you An airplane flying horizontally at an altitude of 3 ... A: Sorry about that. From before, x² = √(3²+4²) = √25 = 5. As pointed out, that's only the ... | |
| Proves | 5/16/2009 |
| Q: Prove: Limit 1/(x+1)= 1/4 x->3 A: Now to prove this proof. Let's turn the fractions upside down. Prove lim(x->3) x+1 = 4. Take any ... | |
| Proving limits | 5/16/2009 |
| Q: Prove: Limit as x approches infinity of 1/((x^2) + 1) =0 Please help. Thanks A: Choose ε and take x > δ. If ε = 1, to make 1/(x²+1) < 1, δ can be chosen as 0. ... | |
| higher derivatives with ordinary language | 5/15/2009 |
| Q: Sorry I'm sending another message, The previous one I sent I ended up getting both answers..so you ... A: Don't worry about it - some people have sent well over 30 messages. For some, this is their third ... | |
| higher derivatives | 5/15/2009 |
| Q: How do I find the 3rd derivative of the second derivative that I got, f''(x)= ... A: 1. Give f(t) = (t²+1)^0.5, f'(t)=(0.5/(t²+1)^0.5)2t = t/√(t²+1). Given this quotient rule, it ... | |
| higher derivatives | 5/15/2009 |
| Q: How do I find the 3rd derivative of the second derivative that I got, f''(x)= ... A: I need to see what the original function was. Basically, if you have f²(g(h(x))), the deritvae is ... | |
| polynomials | 5/14/2009 |
| Q: how do you solve this? find a cubic functions that had a local maximum value of 3 at -2 and a local ... A: This means that the derivative is 0 at x = -2 and x = 1. hat will say that the derivative is of the ... | |
| word problem help! | 5/13/2009 |
| Q: 1)A fence 3 feet tall runs parallel to a tall building at a distance of 2 feet from the building. ... A: 1. You can draw a triangle with base A+2 and height H. The height H would be for the building. The ... | |
| Calculus | 5/13/2009 |
| Q: i need help with problem please, thank you An airplane flying horizontally at an altitude of 3 ... A: If the plane is moving at 480 mi/hr, use 30 seconds to compute how far it traveled. (480 ... | |
| word problem with deriv's. | 5/13/2009 |
| Q: how do I do this, using derivatives? Find the dimensions of the rectangle of largest area that can ... A: Lets put the bottom side of this triangle on the x axis. In fact, let's position it so the center is ... | |
| Calculus | 5/13/2009 |
| Q: I really need help on this question please, because this is my second time posting it and i hope ... A: The derivative says the slope. THe derivative is 3x² + a. When a real number is squared, a positive ... | |
| Min. and Max. problem | 5/11/2009 |
| Q: Please help on the question, What is the maximum volume of a cup of a given surface area S, in the ... A: S = πr² + 2πrh where r is the radius and h is the height. From here, it can be said that ... | |
| critcal numbers | 5/11/2009 |
| Q: Sorry I should have added this to my previous question because they are similar.. my question is ... A: Let g(x) = x². Then g'(x) = 2x. Let h(x) = e^(14x). Then h'(x) = (d(14x)/dx)e^(14x) = 14e^(14x). ... | |
| Critical Values | 5/11/2009 |
| Q: For this: 4x(sqrt(4x^2+2)) How do I get the derivative?? I used the product law, then the chain ... A: It looks like the product of two functions, call them f(x) and g(x). The definition of the two ... | |
| Derivation | 5/10/2009 |
| Q: My book has an exercise that says: Find dV/dp for this equation. Suppose that T and n are ... A: The formula given is PV = nRT(1 + nB/V). Now I remember PV = nRT, but there is a little extra ... | |
| Standard deviation | 5/8/2009 |
| Q: I need help answering this question. Birth weights are normally distributed in Norway with mean of ... A: Using a table for the Normal Distribution (they're found in lots of places), find where 2% are ... | |
| calc | 5/8/2009 |
| Q: how do i find this derivative.. 7cosx(sin(x^3)) This is what I did: ... A: The symbol '*' is for multiplication. I will attach a picture to describe the function as I see it. ... | |
| precalc | 5/8/2009 |
| Q: okay i found that I am stuck on thes questions I solved the answer to some but have no idea if they ... A: Pie tastes good and is not square. The surface area is not round, for pie are square. It is actually ... | |
| calc | 5/7/2009 |
| Q: how do i find this derivative.. 7cosx(sin(x^3)) This is what I did: ... A: Given f(x) = 7cosx(sin(x^3)), find f'(x). Is that f(x) really suppose to be 7cos(sin(x^3)) without ... | |
| Circle | 5/7/2009 |
| Q: Scotto, I just wonder that if there was a circle without center? Say, not in Euclidean Geometry, but ... A: I'm not sure about that. I believe the only way to define a circle is the set of all point that are ... | |
| derivatives | 5/7/2009 |
| Q: hey, another questions on derivatives, find dy/dx given that y^5+y^3+y-x=0 Im just not sure how to ... A: When dy/dx is said, it means the derivative of y with repect to x. It is written that way for a ... | |
| calc w/ trig differentiation | 5/6/2009 |
| Q: given y=sinx(1-cosx) show dy/dx=(1+2cosx)(1-cosx) A: This is a product rule. The product rule states that if y = f(x)g(x), then y' = f'(x)g(x) + ... | |
| derivatives | 5/6/2009 |
| Q: hey, another questions on derivatives, find dy/dx given that y^5+y^3+y-x=0 Im just not sure how to ... A: Take the derivative with the chain rule for each term. This means that every term with a y will be ... | |
| Non Integrable functions | 5/5/2009 |
| Q: I tried much to find the value of the integration of (e^X^2) A: There is no way to integrate e^(x²). However, if you're integrating e^(-x²) from -∞ to ... | |
| Trigonmetry | 5/5/2009 |
| Q: I've being asked to reduce the express to a single term_ sinx*cos2x+sin2x*cosx can you help me ... A: With (1 - cos(2x))/2, that is the same as (1 - 12/13)/2. Now 1 is 13/13, so when we subtract off ... | |
| precalculus | 5/5/2009 |
| Q: A graph of a parabola has line of symmetry x=3 and contains the points (5,-3) and (-1,9). determine ... A: Look at y = a(x-h)² + k. For this parabola, it can be seen that the minimum would be at x = h, ... | |
| Integral of Exponential Function | 5/4/2009 |
| Q: If y = exp(-0.5x^2), what's the integral of y with respect to x? In general, what's the integral of ... A: There is no way to do this integral with finite limits. However, if the integral is from -∞ to ... | |
| calculus | 5/4/2009 |
| Q: find all extrema in the interval [0,2pi] if y = x + sinx A: To do this problem, you need to find y' and set it equal to 0 and also check the endpoints. y' = 1 ... | |
| Have One Problem Qs.. | 5/4/2009 |
| Q: An orchard contains 61 peach trees with each tree yielding an average of 55 peaches. For each 8 ... A: An addition of 8 trees and a loss of 12 peaches is the same as an addition of 2 trees and a loss of ... | |
| Trigonmetry | 5/3/2009 |
| Q: I've being asked to reduce the express to a single term_ sinx*cos2x+sin2x*cosx can you help me A: It is known that sin2x = 2 sinx cosx. It is also known that cos2x = cos²x - sin²x. This converts ... | |
| integrals | 5/2/2009 |
| Q: i should know how to do this but im having a mind blank and keep getting the wrong answer find the ... A: ⌠ ⌡ x dx = x²/2 + C1, ⌠ ⌡ 4x² dx = 4x^3/3 + C2, ⌠ ⌡ x√x ... | |
| derivatives | 5/2/2009 |
| Q: 1.how do I do, find f'(x) f(x)=4xsinxcosx 2. how do I find f'(x) of f(x)=2secx+2(e^x)tanx and ... A: 1. The product rule. Let m(x) = 4sinx and n(x) = cosx. It can be seen that m'(x) = 4cos(x) and n'(x) ... | |
| derivatives. | 5/2/2009 |
| Q: find the equation of a tangent line to the curve y=6sinx at the point (pi/6,3). The equation to this ... A: The tangent line slope is given by the derivative of 6sin(x) at the point x = π/6. The ... | |
| just some random things | 4/30/2009 |
| Q: anything you can answer REALLY DOES HELP! So first part is: 1. to this trig identity, ... A: 1. to this trig identity, sin(x+h)=sin(x)cos(h)+cos(x)sin(h).. by using factoring and limit laws how ... | |
| identity | 4/30/2009 |
| Q: verify the identity: -sin2x+sin6x/sin2x-sin6x= tan4x cot2x A: Try letting u=2x. The problem is then (-sinu + sin3u)/(sinu-sin3u) = tan2u cotu. On the left side, ... | |
| proving | 4/29/2009 |
| Q: So how do I prove this: Find the limit lim Sinx x-> Infinity ------- ... A: So how do I prove this: Find the limit lim Sinx x-> Infinity ------- ... | |
| calculus 1 | 4/28/2009 |
| Q: A person earning $15 per hour is paid only for the actual time on the job. How close to 8 hours must ... A: If they work one hour, the earnings are $15. If they work two hours, the earnings are $15*2 = $30. ... | |
| Math Calculus Qs..thanks you | 4/28/2009 |
| Q: 1. Find the dimensions of the largest rectangle whose perimeter is 3200 feet. (Enter the dimensions ... A: 1. Find the dimensions of the largest rectangle whose perimeter is 3200 feet. (Enter the dimensions ... | |
| calculus | 4/27/2009 |
| Q: ive recently got a question to find the points of inflexion, local maxima and minima, and any ... A: This is a product rule with g(x)=e^n and h(n) = n²+2n+1. The derivative is g(n)h'(n) + g'(n)h(n). ... | |
| antideravitives | 4/27/2009 |
| Q: I need a little help on this homework question, i'd apreciate if you'd help... thank you. A car ... A: We know that the car starts at distance 0. Acceleration is the derivative of velocity. ⌠ ... | |
| Integration problem | 4/27/2009 |
| Q: My problem is integral of (x^3 + 5x^2 - 10x - 8)/(x^3 - 4x) I'm pretty sure i'm supposed to start ... A: Divide it in once, so the power on top is less. The result is (x^3 + 5x² - 10x - 8) - 1(x^3 - 4x) = ... | |
| calculus sequence | 4/26/2009 |
| Q: determine if converges or diverges and which test (2n^2+3n) / (sqrt(5+n^5)) A: Using the power test, the greatest power in the numerator is 2 and the greatest power in the ... | |
| Calculus | 4/24/2009 |
| Q: what is the integral from 2 to 3 of 1/(x^2-4x-5)? A: Wow! Such a long answer for such a little bitty question. Let's look at x²-4x-5. If that were ... | |
| Optimization | 4/23/2009 |
| Q: Ship A is 15 miles east of O and moving west at 20 mi/h, while ship B is 60 mi south of O and moving ... A: Ship A equation: 15-20t miles to the east where t is hours. Ship B equation: 60-15t miles to the ... | |
| Cal II. Vectors | 4/22/2009 |
| Q: "Find a vector valued function that represents the curve C of intersection of the surface ... A: If 2z=y, then z=2y. Finding the intersection with the equation z² = x² + y² can be done by putting ... | |
| limits. | 4/21/2009 |
| Q: Let f(x) = |x-10|. Evaluate the following limits. a) lim f(x)-f(10) x->10- ---------- ... A: On that last question, I don't think you have gotten to derivatives yet, but since I've gotten to ... | |
| rate of speed. | 4/21/2009 |
| Q: If an arrow is shot straight upward on the moon with a velocity of 58 m/s, its height (in meters) ... A: The height of the arrow is s(t). The velocity of the arrow is the derivative of s(t), which I will ... | |
| Rotations | 4/21/2009 |
| Q: I am somewhat confused, so any help would be greatly appreciated! For the region bounded by ... A: The two curves intersect. Set them equal to find where. That's 2 + 1/x = -x + 6. Moving ... | |
| Infinite series problem | 4/20/2009 |
| Q: Hey Scotto, I have a word problem pertaining to infinite series that I have no clue how to do. Here ... A: I hope someone else could give you a solution to this. I also pray you're having a good day. There ... | |
| Calculus,tangent line | 4/19/2009 |
| Q: Find the tangent line(s) to the curve y=x^3-9 through the point (1,-9) A: The tangent line needs the same slope as the curve at the point where it touches the curve. Take ... | |
| Calculus | 4/19/2009 |
| Q: use logarithmic differentiation to find dy/dx find y' if y= x^2(sin^-1x)^3 A: From what I remember of logarithmic differentiation, it goes something like this: You say that ... | |
| Precalculus | 4/19/2009 |
| Q: Solve for x: log 3 (tan x) = 1/2. tan x = the square root of 3 A: It can be seen that tan x = √3. This means that if the far side is √3, the near side ... | |
| Calculus | 4/18/2009 |
| Q: integrate: sin(1/x)/3x^2 A: When problems like this are seen, note that the derivative of what inside the sin() is almost on the ... | |
| Pre-Calculus - Trig Identities | 4/18/2009 |
| Q: I'm having trouble with a couple of questions. Can you please help me? 1. sinx/1-cosx + ... A: 1. Get a common denominator. That gives (sin²x + (1-cosx)²) / (sinx(1-cosx)). Numerator Hold on ... | |
| NEED HELP ASAP | 4/18/2009 |
| Q: If a ball is thrown straight up into the air with an initial velocity of 50ft/s its height in feet ... A: As can be found in http://en.wikipedia.org/wiki/Gravity, the force of gravity is 32.2. That gives ... | |
| Calculus | 4/16/2009 |
| Q: What is the area of the region enclosed by the graphs of f(x) = x - 2x^2 and g(x) = -5x? A: First we have to know where they cross. If we set 5x = 2x² - x, we get 0 = 2x² -6x, so we can see ... | |
| Calculus | 4/16/2009 |
| Q: I needed help on this homework problem, would apreciate if you could help me, thanks What is the ... A: The slope of f(x) = x^3 - 3x² + 5x is the derivative of the function. The derivative f'(x) = 3x² - ... | |
| calculus | 4/16/2009 |
| Q: I am in calculs and i need help with this homework problem please... If functions f and g are ... A: The first question is answered in a JPG file and should be attached. I can do 2 right here. let y = ... | |
| Deceleration | 4/15/2009 |
| Q: A car is traveling at 50 mph when the breaks are fully applied, producing a constant deceleration of ... A: To start with, convert 50 mph to ft/sc. To do this, take 50 miles/hour and do the following: (50 ... | |
| calculus | 4/13/2009 |
| Q: Use calculus to aid you in sketching the graph of f(x)=x·√{x+1}. for what values of x is f(x) ... A: Note that √ os the same as ^(1/2) and that x^(-a) = 1/x^a. The values where f(x) is defined ... | |
| Even and Odd Functions | 4/13/2009 |
| Q: I was wondering if you could help me out on even and odd functions. My question is how can you tell ... A: For an even function, the exponets must all be even. for an odd function, the exponets must all be ... | |
| calculus - derivatives | 4/13/2009 |
| Q: im trying to find the derivative of (1/2)tan^-1(x/2) - (1/3)tan^-1(x/3) also does tan to the power ... A: The -1 means the iverse. If x = tan(Θ), then Θ = tan^-1(x). If we integrate x = ... | |
| geometry | 4/12/2009 |
| Q: how many points are sufficient to draw a straight line ANSWER: If you only had one point, any ... A: No, since with only one point, it doesn't determine which way the line goes. If you have a graph ... | |
| Problem set in summer class calculus 3 | 4/11/2009 |
| Q: 1.) Find the equation of the line that passes thru (5, -8) and will form the largest triangle with ... A: y is in radians ------------------------------- On the question, note that (sin180y)/y is the same ... | |
| geometry | 4/10/2009 |
| Q: how many points are sufficient to draw a straight line A: If you only had one point, any other point would be on a line with it. If there were two points, ... | |
| Sinusoidal function | 4/10/2009 |
| Q: How do u find an equation for a sinusoidal function that has been graphed A: The function has an average. Let this be where y is 0. The function needs to start at 0 to be a ... | |
| Problem set in summer class calculus 3 | 4/8/2009 |
| Q: 1.) Find the equation of the line that passes thru (5, -8) and will form the largest triangle with ... A: 1.) Find the equation of the line that passes thru (5, -8) and will form the largest triangle with ... | |
| Limit Question | 4/7/2009 |
| Q: lim ((x-2)^7)(-2x^2) x->1 So for this, I got a limit of 2, but I need to state all the limit ... A: The lim as x->1 of x-2 is -1. You can do this by direct substitution. When -1 is taken to the 7th, ... | |
| Limit Question | 4/7/2009 |
| Q: lim 1/x - 1/4 x->4 --------- x-4 When I do this, I get the denominator of zero, ... A: Multiply the top and bottom by 4x. On top the result is 4 - x. On bottom, leave the result as ... | |
| Problem | 4/6/2009 |
| Q: Hey Scotto, I need help for the following word problem: Suppose that you draw a 2" x 2" square, ... A: I can't find the image from my computer anywhere on the internet. I tried the full image name and ... | |
| Error bars | 4/6/2009 |
| Q: I'm trying to get error bars on my bar chart in Excel. The graph is showing the mean number of eggs ... A: The sample is the number of eggs each day. The mean is the average number of eggs each day. If ... | |
| Integrate | 4/5/2009 |
| Q: can u please show me the steps on how to integrate the following questions... (4sqrtx^3) + 1) dx ... A: I will assume you are suppose to integrate(4*x^(3/2)+1)dx. Add 1 to the exponet and divide by the ... | |
| Trigonometry | 4/5/2009 |
| Q: You are on a fishing boat that leaves its pier and heads east. After traveling for 30 miles, ... A: a. The boat went 30 miles to the east. It turns and heads south bearing 45 degrees west for 12 more ... | |
| Derivative and Absolute Minimum | 4/4/2009 |
| Q: The derivative of f is given by f'(x) = e^x(-x^3+3x) - 3 for 0 <= x <= 5. At what value of x is ... A: When a function f is at an absolute minimum, then f' is zero at that point and f" is negative. ... | |
| Normal Line To Curve | 4/4/2009 |
| Q: The equation of the normal line to the curve y = (x^2 - 1)^(1/3) at the point where x = 3 is a. y ... A: To find this, the equation must have the same slope. To find the answer, take the derivative and put ... | |
| statements... | 4/3/2009 |
| Q: How do I graph this??? f(x)= (7 if x>2 3 if x=2 -x+7 if -5 less than or ... A: At all x values to the left of -5, but in the line y=12. Between x=-5 and x=2, put y=-x+7. At ... | |
| calculus | 4/2/2009 |
| Q: I have to find the area of the shaded region by integrating using dy. I just have to set up the ... A: Doing just one interval of integration won't cut it. As the picture shows, you need to evaluate two ... | |
| Integration | 4/2/2009 |
| Q: { <- integral sign d/dx {sin(t^2) dt upper limit -> x^3 lower limit -> x a. sin(x^6) - sin(x^2) b. ... A: The actual integral sign is ⌠, alt-244, and ⌡, alt-245. The derivative is the opposite ... | |
| Implicit Differentiation | 4/2/2009 |
| Q: If x + y = xy, then dy/dx is a. 1/(x-1) b. (y-1)/(x-1) c. (1-y)/(x-1) d. x + y - 1 e. (2-xy)/y A: To take the derivative of x + y = xy, note that y is a function of x. As such, the derivative of x ... | |
| Height of a circle segment | 4/1/2009 |
| Q: Given a circle with a radius of 50.75", and a segment of that circle has an area of 3000 sqin. ... A: What you are gives is r = 50.75, the radius of a circle. The total area of a circle is given by A = ... | |
| Cal II. Vectors | 4/1/2009 |
| Q: Describe the region of R^3 represented by the inequality x^2+y^2+z^2>2z A: The equation should be transformed into what I can understand. The eqatuion x² + y² + z² = 2z needs ... | |
| Calculus Finding derivative | 4/1/2009 |
| Q: If y = x^(x^3) for x > 0, then find dy/dx A: This is almost like a product rule, except that it is an exponential problem. Read slow and ... | |
| Optimization Problem | 4/1/2009 |
| Q: An open box is to be made from a rectangular piece of material by cutting equal squares from each ... A: In this problem, the height of the box is x. Since this needs to be cut out of all corners, it ... | |
| percent question | 3/31/2009 |
| Q: I work in customer service for a finance company. Im often asked a question by customers on what ... A: Divide 3000 by 2400 and subtract 1, and then multiply by 100. That would give the interest rate. ... | |
| calculus-integration | 3/30/2009 |
| Q: I need to integrate the following: sqrt(2-2cost) dt A: This looks like a u substitution problem with u = -cost. Troulble is, we need a sint in the problem ... | |
| Calculus - Min/Max | 3/30/2009 |
| Q: You are designing a rectangular poster to contain 256 in^2 of printing with a 3" margin at the top ... A: It has width W and height H. WH=256. With the perimeter, it's (W+2+2)(H+3+3) = (W+4)(H+6). We can ... | |
| calc | 3/30/2009 |
| Q: THEIR THE PROVIDE THE IDENTITY: 1. SEC^2X-TAN^2=1 2. SIN^2X/(1-COSX)^2=1+COSX/1-COSX 3. ... A: 1. To make the left side look like 1, note that sec²x is 1/cos²x and tan²x is sin²x/cos²x. Combing ... | |
| Arc Length function | 3/29/2009 |
| Q: Compute the arc length function for the curve y=f(x)=e^x relative to it's y intercept. A: To compute the arc length, you need to integrat from the y inercept to the point on the graph ... | |
| Vectors | 3/29/2009 |
| Q: 1. Why does the vector equation of a plane have two parameters while the vector equation of a line ... A: Sam 1. Why does the vector equation of a plane have two parameters while the vector equation of a ... | |
| calculus | 3/27/2009 |
| Q: For the equation given below, evaluate [dy/dx] at the point (25,25). √x+√y = 10 ... A: You can do this with implicit differentiation or by finding y exactly. Implicitily, 1/(2√x) + ... | |
| calculus | 3/27/2009 |
| Q: Fnd the equation of the line tangent to the curve xy^3+xy = 8 at the point (4,1). When the ... A: To find m, you need y'. To find y', differentiate. Now that both xy^3 and xy are product rules. ... | |
| differential equations and separation of variables | 3/27/2009 |
| Q: If dy/dx = x^3 * 1/y(x) and given y(0) = 1, how do you find y(x)? A: Multiply both sides by y(x) and dx giving y(x) dy = x^3 dx. Make y(x) just y, so you have y dy = ... | |
| Integration | 3/27/2009 |
| Q: Can you help me integrate (x cot(x))dx? Thank you! A: First, I use ctn(x) instead of cot(x). That way, I'm sure not to get it confused with cos(x). ... | |
| trigometric expressions | 3/24/2009 |
| Q: I have come across some problems in math for a placement test for college and i have no idea what to ... A: 1. If the cos(x) = a/3, the hypotenuse of the triangle has length a and the near side has length 3. ... | |
| related rates | 3/24/2009 |
| Q: All edges of a cube are expanding at the rate of 3 cm per second. How fast is the surface area ... A: A cube has six faces. The lenth of each side is x. The surface area of each face is x². There ... | |
| Calculus How derivatives affect the shape of a graph | 3/23/2009 |
| Q: Will you please help me figure out these things I cant figure them out. Thank you so much. given ... A: The function given is f(x) = (9√x)e^(-x). The derivative of this function is done by use of ... | |
| derivative of e^(1/2*x) | 3/22/2009 |
| Q: Why is the derivative of e^((1/2)x) 1/2e^((1/2)x)? I thought the rule was f'(e^kx)=(e^kx)/k. ... A: From the chain rule, we know that the derivative of f(g(x)) is f'(g(x))g'(x). Here, f(x) is e^x and ... | |
| Min/Max problems | 3/22/2009 |
| Q: An open box of maximum volume is to be made from a square piece of material, 24 inches on a side, by ... A: Let us assume that the base of the box is x (some number less than 24). This would give leave 24-x ... | |
| Hi, I've got two questions | 3/22/2009 |
| Q: I was given the following questions: I) Find the slope of the tangent line to the curve (a ... A: I) Find the slope of the tangent line to the curve (a lemniscate) 2*(x^2+y^2)^2=25*(x^2-y^2)at the ... | |
| Correct to my Questions (Implicit Differentiation) | 3/21/2009 |
| Q: 1. Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at ... A: Now the correct answer to the first 4 I just sent and then I was this corrected case. What I will ... | |
| Implicit Differentiation Help! | 3/21/2009 |
| Q: 1. Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at ... A: 1. Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at ... | |
| Calculus Problemss | 3/20/2009 |
| Q: 1. For the given cost function C(x)=5300+340 x + 1.7 x^2 and the demand function p(x) = 1020. Find ... A: 1. For the given cost function C(x)=5300+340 x + 1.7 x^2 and the demand function p(x) = 1020. Find ... | |
| pre-cal please | 3/20/2009 |
| Q: how do you simplify (1-sin^2 x)(91-tan^2 x)? I'm really sorry if it isn't in the right format. A: We know that 1-sin²(x) = cos²(x). Is that second term suppose to be 91-tan²(x)? If it is, then the ... | |
| pootal help please | 3/19/2009 |
| Q: How do I factor : x^3 + 3x^2 + 1 (I set y as zero because i need to find the x intercept to graph ... A: Since x^2 is positive and 1 is positive, the answer must be negative. With the 3x^2 and the x^3, the ... | |
| calculus | 3/19/2009 |
| Q: My qns is: The shape of an ice hill is given by the function f(x,y)=x^3-3xy^2 representing the ... A: You''ve got the gradient written down wrong. The grad f = (3x²-3y², -6xy). What I see is ... | |
| calculus | 3/18/2009 |
| Q: I am Ssa. I am given this function, f(x,y)= √(|xy|). How do I find out if this function is ... A: The function is continuous everywhere since at 0 the function is 0. The | | symbol means that we ... | |
| Trig max/min problems | 3/16/2009 |
| Q: Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, ... A: The derivative of (3 - x)/2 is the same as the derivative of 3/2 - x/2. This derivative is -1/2. ... | |
| prolem | 3/15/2009 |
| Q: I have a problem that says : express sin11pi/12+sin5pi/12 as a product and find the exact value of ... A: We’ll divide these into terms (1) sin(11π/12) and (2) sin(5π/12). 1] Now for the term ... | |
| differential equations | 3/14/2009 |
| Q: I need to apply a differential calculus to economics. I want to use a cost function. How would i set ... A: You can review any of 1-3, but it might be best to look at (3) first. You know, save the bets till ... | |
| Trig max/min problems | 3/13/2009 |
| Q: Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, ... A: We know that if A and B are two angles in a right triangle, then A+B = pi/2. Furthermore, we can ... | |
| Problem with ellipse. Completely lost | 3/13/2009 |
| Q: (x2/a2)+(y2/b2)=1 is the equation for an ellipse with the verticies (+-a,0)(0,+-b) and a slope m ... A: For an ellipse, the equation is really suppose to be (x/a)² + (y/b)² = 1. For (1,1) to be on the ... | |
| Trig max/min problems | 3/12/2009 |
| Q: Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, ... A: I'll use the formula arccot(x) = π/2 - arctan(x). This makes the function Θ(x) = ... | |
| Optimization | 3/12/2009 |
| Q: A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide ... A: The number 3000000 needs a couple of commas I think - I have a hard time counting 0's. 3,000,000 - ... | |
| Calculus integration | 3/11/2009 |
| Q: How do I know when to use integration by parts? My textbook uses ln to solve the integral of ... A: The only way that I have found is by trial and error. Eventually you recognize how to do a lot of ... | |
| Optimization | 3/11/2009 |
| Q: What are the dimensions and the area of the largest rectangle that can be inscribed in a semicircle ... A: The largest rectangle that can be inscribed in a semicirle of radius 2 would be found by taking the ... | |
| problem | 3/10/2009 |
| Q: I have a problem that i can not solve it says use a doule or half angle formula to find the exact ... A: The tan(π/12) can be found with the formula tan(Θ/2) = (1-cos(Θ))/sin(Θ). Note ... | |
| hi | 3/10/2009 |
| Q: how do you solve the triangle?? (rounded two decimal places) b=17.8 c=28.3 B= 27 degrees there ... A: Since we know angle B, the law of cosines says that a² + c² -2ac*cos(B) = b². This will reduce to ... | |
| Taylor series | 3/10/2009 |
| Q: I need help finding the Taylor series for f centered at 1 given f^(n)(1)= (-1/3)^n * (n+1)!/n^(3/2). ... A: The Taylor's series around the point x=1 is this: sum(0 to infinity)(x-1)^n*f^(n)(1)/n!. Now (x-1)^n ... | |
| identity | 3/9/2009 |
| Q: I was wondering could u show me how to idetify this identity: cosx+sinx*tanx=secx A: I convert most everything in trig to sinx and cosx. I know that tanx = sinx/cosx. I also know that ... | |
| calculus | 3/8/2009 |
| Q: lim x->4 2x-8/x^2+16 also, if you don't mind would you check these lim x->4 x^2-16/ x-4 =8 lim X-> ... A: In the first problem you give, the denominator is always (always) positive. The least it gets is ... | |
| calculus | 3/6/2009 |
| Q: proof of limit of lnx = negative infinity as x approaches a from the right A: The lnx is the power of e that is needed to represent a number. To prove that lnx approaches 0 from ... | |
| Question | 3/6/2009 |
| Q: I can not figure this question out it says: Use a double or half angle formula to find the exact ... A: A² is A squared = A*A. √A is the square root of A. The equations to use are tan(B/2) = ... | |
| Question | 3/5/2009 |
| Q: I can not figure this question out it says: Use a double or half angle formula to find the exact ... A: The exact value is known of that tan(π/3). Using the half angle formula on this will give you ... | |
| Verify the Identity | 3/5/2009 |
| Q: cosx +sinx*tanx = secx A: Put in tanx = sinx / cosx. Multiply the cosx by cosx/cosx so you have cos²x/cos. Combine the ... | |
| One more Calculus question in this sections | 3/3/2009 |
| Q: I have one more question to finish this section. Your help is greatly appreciated: A light shines ... A: Here we have similar triangles. The height of the big triangle is H = 35 ft. The height of the ... | |
| Calculus | 3/3/2009 |
| Q: Problem driving me crazy. Please help. Two airplanes (at the same height) are flying away from an ... A: They are at right angles. The side with Y is 190 mi. The hypoteneuse is 500 mi. The other sides is ... | |
| help | 3/2/2009 |
| Q: can u solve this problem and show the steps for me 2 understand............x+2y+z=-1 ... A: To do so, take the matrix of coefficients with the constants at the end of each row. What you have ... | |
| calculus | 3/2/2009 |
| Q: Let f be the function defined for pi/6 ≤ x ≤ 5pi/6 by f(x)=x+ (sin x)^2. a. Find all ... A: We know f'(x) = 1 + 2(sinx)cosx bu use of the chain rule on f(x). Set this to 0 to find maximums, ... | |
| Introductory Material | 3/2/2009 |
| Q: , My name is Gonzalo Gil and I just completed my undergraduate work in Econ/PolSci. I am writing ... A: When I was in college, we used a textbook that is probably outdated since it was 20 years ago. Now ... | |
| Complex numbers in argument form | 3/1/2009 |
| Q: (i)two complex numbers z_1 & z_2 are given by z_1=10-2i & z_2=2-3i.Show that z_1/z_2 is of the form ... A: i) Multiply the top and bottom by the conjugate of the bottom to convert to real form. The bottom ... | |
| Complex numbers in algebraic form | 3/1/2009 |
| Q: Find the complex number z with the least positive argument satisfying the condition |z-25i|<=15. ... A: The absolute value, when in complex for, is √(a²+2ab+b²). The absolute value of this number ... | |
| Complex numbers | 3/1/2009 |
| Q: (i)Find the modulus & argument of each of the complex numbers z= (1+i)/(1-i) & ... A: For both variables, multiply by the conjugate of the denominator. That is, multiply the numerator ... | |
| Reply soon with in 12 hours please: Derivates | 3/1/2009 |
| Q: I need help with this: the question is: Determine the equation of the tangent y=1/2x^2-x-1/3 that ... A: I've seen people close the comment with a smiley face, but what I see in yours is a =P. Maybe that ... | |
| Reply soon with in 12 hours please: Derivates | 2/28/2009 |
| Q: I need help with this: the question is: Determine the equation of the tangent y=1/2x^2-x-1/3 that ... A: The slope of 8-3x is -3, so the slope of the perpendicular has the inverse of -3, which is -1/3. To ... | |
| Domain and Ranges of Inverse functions | 2/27/2009 |
| Q: Scotto can you please help me on thisConsider this function y=3x-1/2x on restricted domain ... A: To find the range, not that the domain is all x in (-infinity,0). I will assume the function is y = ... | |
| calculus | 2/26/2009 |
| Q: prove that,if the sum of the radii of two circles remains constant,the sum of the areas of the ... A: R is the total of circles with radius S and T. Note that T = R-S. The total area is π(S² + ... | |
| fourier transform | 2/26/2009 |
| Q: for the fourier transform attatched I need to determine expressions for the amplitude and phase of ... A: For amplitude and phase, usually there is a trig function involved. This function is going to 0 as w ... | |
| trig | 2/25/2009 |
| Q: how many pounds of 65% hth chlorine are required to disinfect a 6 inch water main, 600 feet long ... A: If you mean to fill the entire pipe with the chlorine mixture, I will assume that 6 inches is the ... | |
| roots | 2/25/2009 |
| Q: express answers in a+bi.. x^6 + 729 = 0 I did x= sqrt(-729) x= i sqrt(729) x= 3i (3i ... A: We have x^6 + 729 = 0, or x^6 = -729. Note that the answer is already at π degrees in polar ... | |
| fifth root | 2/25/2009 |
| Q: Find the fifth roots of the given number in polar form. (List your answers counterclockwise starting ... A: What does ^5sqrt(15) mean? The 5th root of 15? The angles you got were correct, but you forgot k=0. ... | |
| Fluid Force | 2/24/2009 |
| Q: Scotto can you please tell me what l am doing wrong on this question is has been giving me headaches ... A: I would appreciate it if the writing non the paper was a little bit darker. It's almost all ... | |
| Density functions | 2/24/2009 |
| Q: The standard deviation for a random variable with probability density function f and mean mu is ... A: From the definition of the exponential, mu and sigma are 1/lambda. To compute it, use your ... | |
| Fluid Force | 2/23/2009 |
| Q: Scotto can you please tell me what l am doing wrong on this question is has been giving me headaches ... A: What I have used int() for is the integral (not integer less than). 2pg*int(0 to ... | |
| equations | 2/22/2009 |
| Q: If you could help me that would be great! 7(y+2)+8(y+3)+21= -76 please walk me throught the steps! ... A: Each set of parenthesis needs to have the factor multiplied on each of the elements inside. ... | |
| Integration | 2/21/2009 |
| Q: I have been working on this integration problem, but I'm not getting anywhere. Could you show me the ... A: Factor out the -1/3 on top, giving (-1/3)(x+1)/(x²+x+1). Note that the derivative of the bottom is ... | |
| Applications of Derivatives | 2/21/2009 |
| Q: The spread of a virus is modeled by N=-t^3+12t^2, 0<=t<=12, where N is the number of people ... A: It gives the equation for spread of a virus. It asks when it will spread most rapidly. This would ... | |
| Inverse of function | 2/20/2009 |
| Q: y=3x-1/2x Attempt to solution: y=(6x^2-1)/(2x) x= (6y^2-1)/(2y) 2yx=6y^2-1 2yx-6y^2=-1 ... A: Soory about that, but several people incorrectly put parenthesis in the problem. I have seen that ... | |
| differential calculus | 2/20/2009 |
| Q: what is the derivative tan(arcsin(x))? Thanks A: That is a chain rule. The derivative of tan(f(x)) is sec²(f(x))f'(x). Here, we have f(x) = ... | |
| Inverse of function | 2/20/2009 |
| Q: y=3x-1/2x Attempt to solution: y=(6x^2-1)/(2x) x= (6y^2-1)/(2y) 2yx=6y^2-1 2yx-6y^2=-1 ... A: Multiply the entire equation by 2x to get 2xy = 3x – 1. Add 1 to both sides, giving 2xy + 1 = 3x. ... | |
| Inverse of function | 2/19/2009 |
| Q: y=3x-1/2x Attempt to solution: y=(6x^2-1)/(2x) x= (6y^2-1)/(2y) 2yx=6y^2-1 2yx-6y^2=-1 ... A: Here is how to find the inverse function. Instead of expressing y in terms of x, we will express x ... | |
| Integration | 2/19/2009 |
| Q: How do l integrate this : F= ∫(20 cos t+ 8 sin t cos t) TIMES 2 cos(t) dt A: Multiply the integral out, giving ∫40cos²(t) dt + ∫16sin(t)cos²(t) dt. Differentiate ... | |
| Relative maxs & mins, points of inflection | 2/19/2009 |
| Q: 1.) Determine the following about the graph of the equation y= (8/x^3)-(6/x). b.) Find the ... A: I won't go over the answers given since a simpler approach would be to say the 8/x^3 = 8x^(-3) and ... | |
| linear motion | 2/18/2009 |
| Q: a sled is initially moving at a rate of 44 ft/sec. it decelerates to 32 ft/sec over a distance of ... A: We know that the equation is v(t) = 44 + (32-44)t/N for some t with N as the amount of time to get ... | |
| surds | 2/18/2009 |
| Q: can you help me learn how to do this surd? 1/3+root 2 in words= one,divided by three plus the square ... A: The answer is wrong with the way the question is written. It looks like they really meant the ... | |
| surds | 2/18/2009 |
| Q: can you help me learn how to do this surd? 1/3+root 2 in words= one,divided by three plus the square ... A: If that 1/3 and then add √2, which is the same as √2 + 1/3, or 1/(3+√2)? I think ... | |
| i'm stuck | 2/18/2009 |
| Q: Find all the roots of f(x) in the complex number system; then write f(x) as a product of linear ... A: Find all the roots of f(x) in the complex number system; then write f(x) as a product of linear ... | |
| Fluid Force | 2/17/2009 |
| Q: A circular "pressure release gate" is located in the vertical face of a dam. The radius of the gate ... A: The depth of the opening has radius 2 meters, which means it's diameter is 4 meters. Since x is our ... | |
| Calculus Word Problems | 2/17/2009 |
| Q: 1The number of bus riders from the suburbs to downtown per day is represented by 1200(1.50-x), where ... A: 1. Take 1200(1.50-x) times x. Take the derivative, set it equal to 0, solve for x. This is the ... | |
| Fluid Force | 2/17/2009 |
| Q: A circular "pressure release gate" is located in the vertical face of a dam. The radius of the gate ... A: WE need to integrate the width * depth from one side of the cylinder to the other. This means we ... | |
| Difference Quotient Calc | 2/16/2009 |
| Q: Find and Simplify your answer. F(x)=x^3 +3x, F(x+h)-F(x)/h, H=/0 A: Put x+h into the fuction and put x into the function. Subtract the second from the first. Divide the ... | |
| Moments and Center of Mass | 2/16/2009 |
| Q: A lamina with uniform density p= 18 is bounded by the curve 9x-x2 and the x axis. Give moments and ... A: I found in libraryofmath.com/moments-and-center-of-mass.html that ⌠ ⌡yf(x) dA = Mx and ... | |
| Work Problem- Conical Tank | 2/16/2009 |
| Q: Conical Tank is 5 feet wide at the top, 2 feet tall. How much work to fill the entire tank from ... A: The volume of a cone is πr²h/3. We know that 2r = 5, h = 2 and π=3.1416 (roughly), so the ... | |
| Trig - Unit Circle | 2/16/2009 |
| Q: I hope that my question actually makes sense. I am in the 11th grade and we are studying ... A: It is known that a circle is 360°. It is also known that a circle is 2π radians. This means ... | |
| calculus | 2/15/2009 |
| Q: the number of bus riders from the suburbs to downtown per day is represented by 1200(1.5-x) where x ... A: It is known that the total fare is pN where p is the price for each one and N is the total ... | |
| Simpsons Rule applied to biology | 2/13/2009 |
| Q: After an 8-mg injection of dye, the readings of dye concentration, in mg/L, at two-second intervals ... A: Simpson's rule states that on any interval (a,b), the integral of f(x) on (a,b) is (b-a)(f(a) + ... | |
| q | 2/13/2009 |
| Q: How do I show that sinx-secx=0 has no solutions? Also how do I solve sinx=cosx A: It is known that |sin(x)| <= 1. It is known that |sec(x)| >= 1. It is also known the sec(x) = ... | |
| Calculus Integration | 2/12/2009 |
| Q: Ok hello again. My question is I have to integrate & e^(- 3x) when x goes from 1 to infinity . So I ... A: To integrate e^(-3x), all you've got to do is to divide by the multiplier. The answer is ... | |
| Calculus | 2/12/2009 |
| Q: A swimmer crosses a river starting at point A and ending at point B, following the path shown below. ... A: The distance swam from A to B will be known as 1. When the swimmer starts out, the distance ... | |
| Calculus | 2/12/2009 |
| Q: For each of the following fuinctions from S to R (with f(x) being set to 0 whenever the definition ... A: Note that when sets of questions come my way, I sometimes don't answer them since I have too many ... | |
| maths | 2/12/2009 |
| Q: limit as x approaches 0(e^x-sinx/x-sinx) A: If you remember from elementary mathematices, powers are done first, then division, and then the ... | |
| elemantary calculus | 2/11/2009 |
| Q: Maximum Profit: assume that the amount of money deposited in a bank is proportional to the square of ... A: Amount of money is M. Interest rate is i and ki² = M, where k is a constant. The bank can invest ... | |
| problem. | 2/10/2009 |
| Q: Use factoring, the quadratic formula, or identities to solve the equation. Find all solutions in the ... A: If you let a = cos(x), there is the quadratic 5a² + 17a - 12 = 0. This, as you stated, factors into ... | |
| word problem | 2/10/2009 |
| Q: A camera on a h = 5 foot high tripod is placed in front of a m1 = 7 foot high picture that is ... A: The angle Θ should be so that the camera looks into the middle if the image. Let the distance ... | |
| help. | 2/10/2009 |
| Q: When a light beam passes from one medium to another, (for instance, for air to water), it changes ... A: The equation is sin(Θ1)/sin(Θ2) = V1/V2. We have been told that Θ1 = 29° and that ... | |
| 3d vectors | 2/9/2009 |
| Q: the line l_1 passes through the point A,whose position vector is i-j-5k, & is parallel to the vector ... A: Line L1 is (1,-1,5) + (1,-1,-4)t. Line L2 is (2,-9,-14) + (2,5,6)t. The two points P and Q are P = ... | |
| Vectors 3d | 2/9/2009 |
| Q: I dont understand this topic. Please help me, i need the whole solutions. The points A,B,C and D ... A: A = i - j + 2k B = 3i + 7j - k C = 4i + 15j + 10k D = 2i + 18j + 2k a) To pass through A ... | |
| Vectors | 2/9/2009 |
| Q: i dont know how to get started with this as i dont understand this topic. Please guide me. the line ... A: Line L has the equation r = (7i+0j+3k)+ t(5i+3j+2k) = (7,0,3) + (5,3,2)t. Plane ¥ has equation ... | |
| Calculus-Max & Min | 2/8/2009 |
| Q: You are designing a soft drink container that has the shape of a right circular cylinder. The ... A: Let's assume that the rim around the top and bottom are not worried about. The total surface area ... | |
| Absolute values problems | 2/5/2009 |
| Q: In the past week my teacher started teaching Absolute values to the class. me being a slow learner ... A: Note that when variables (the x value) occur in | |, you need to see where the value in the | | is ... | |
| Absolute values problems | 2/5/2009 |
| Q: i am having sooo much trouble with these absolute value problems. we started them about a week ago. ... A: Absolute values are this: There are only three choices for numbers: +, -, or 0. +: If the number is ... | |
| Integral of exponential functions | 2/4/2009 |
| Q: Proove that the derivative of xe^x= (x+1)e^x by integrating (x+1)e^x. (e^x is an exponential ... A: ⌠ ⌡ dx will be repaced by I()dx I(v du) = uv - I(u dv). Adding the I(u dv) to both ... | |
| Integral of exponential functions | 2/3/2009 |
| Q: Proove that the derivative of xe^x= (x+1)e^x by integrating (x+1)e^x. (e^x is an exponential ... A: There are two ways you could go and both work. Both involve a u-v problem. [1] Let u=x+1 and dv = ... | |
| Calculus | 2/1/2009 |
| Q: I need help.. I have to find the derivative of dy/dx (cos x). I know the answer is -sin x, but I ... A: I copied this out of http://math2.org/math/derivatives/more/trig.htm sin(x) = lim(h->0)(sin(x+h) - ... | |
| max- min optimization | 2/1/2009 |
| Q: An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. ... A: The area of a triangle is known to be bh/2 where b is the base and h is the height. In this ... | |
| ? | 1/31/2009 |
| Q: in the expression y = 63t e^(-64t) the variation of y and time (t) gives a critically damped type of ... A: If the function is 63t e^(-64t), the derivatived is a product rule with f(t) = 63t and ... | |
| Calculus | 1/30/2009 |
| Q: Given y = 2x/(x-3) Find: a) the vertical asymptotes, if any. b) the horizontal asymptotes, if ... A: a) the vertical asymptotes, if any. Vertical asymptotes occur when the function is undefined and ... | |
| Calculus | 1/30/2009 |
| Q: Suppose f'(x) = (x+1)^2 (x-3)^5 (x-6)^4. On what intervals is f decreasing? A: It is increasing wherever f'(x) is positive. Note that anything squared is always positive, so the ... | |
| Calc II | 1/29/2009 |
| Q: Ok I should know this but I can't remember how too. I have to do a long division on x^2/ x+4 and ... A: I wouldn't bother with division. I would let u=x+4, then du = dx. ⌠ x² ⌡x+4 dx is the ... | |
| Hw. Help. | 1/27/2009 |
| Q: Assume the following and evaluate the given expression sin(x)= 12/13, 0 < x < x/2 find. sin(4x)= ... A: sin(2x)=2sin(x)cos(x) Here we have sin(x) = 12/13, so the cos(x) = 5/13. { you know, if one leg is ... | |
| Hw. Help. | 1/27/2009 |
| Q: Find each of the following under the given conditions. (Enter the exact answer as a fraction. ... A: If one leg is 12 and the hypoteneuse is 13, the other leg it the squareroot of (13^2 - 12^2) = ... | |
| Calculus | 1/27/2009 |
| Q: I ran into this problem is integration by parts. the problem is Ln(2x+1) I know u= Ln(2x+1) du= ... A: Note that xln(2x+1)-x +(1/2)ln (2x+1) + C can be rewritten by moving the x to the end and ... | |
| Trigonometry | 1/25/2009 |
| Q: Latasha and Markisha are flying kites on a windy spring day. Latasha has released 250 feet of string ... A: The length of the string is the hypoteneuse of a triangle. We want the far side, so a sin(x) is ... | |
| Inverse function | 1/25/2009 |
| Q: i've encountered a problem in inverse function, can you help me? Q: Show that f(x) is its own ... A: Take some number. You get root(1-x^2). Put this back in the original equation for x. You get ... | |
| Optimization | 1/24/2009 |
| Q: I have a project in my econ class and I want to wow them with some calculus that you might be able ... A: In terms of math, the problem is fairly straight forward. Determine which size house generates the ... | |
| Calculus | 1/23/2009 |
| Q: substitution rule. tan^2x sec^2 x dx I finally reached the pt. where my brain is dead can you help ... A: To solve this problem, remember that d(f^n(x)) = nf^(n-1)(x)f'(x) dx. First note you have a product ... | |
| Calculus | 1/23/2009 |
| Q: A model for the growth of a bacterial culture is given by N(t)= 2+sin^2t+sint for 4<t<8.5 where ... A: To find where N'(t) is so, not that sin2t = 2(sint)(cost). The equation is then 2(sint)(cost) - ... | |
| Calculus | 1/22/2009 |
| Q: Ok I'm reviewing for my class, I took calculus last in 07 I need to refresh my memory on this d/dx ... A: Is the function y = xe^(-1/x)? If so, the derivative is a product rule. f(x) = x and g(x) = ... | |
| Calculus | 1/22/2009 |
| Q: A rectangular field is to have an area of 500 square meters. 1) Write the Perimeter, P, of the field ... A: The width is w and the area is 500, which makes the length l 500/w. The perimeter is twice the ... | |
| Calculus | 1/22/2009 |
| Q: You are living in a time before Newton and Leibniz. One night as you sleep, you have a dream ... A: a) When x is 27cos(theta), note that x is divided by 27. This makes the first term cos^2(theta). ... | |
| Calculus | 1/22/2009 |
| Q: You are the marketing vice president of the bamboo pen tablets company, and you forecast that the ... A: a) The revenue function R is just like it says, R = pq. You are given an equation for q, so all that ... | |
| taylor series | 1/21/2009 |
| Q: I was wondering if you can explain to me Taylor series and how to solve them. If you can in simple ... A: I barely learned it in my third our fourth term of calculus, so it's fairly high in calculus. If ... | |
| help. | 1/21/2009 |
| Q: State the rule of a function of the form f (t) = Asin(bt) or g (t) = Acos(bt) whose graph appears to ... A: I tried putting http://www.webassign.net/hprecalc/6-5-18.gif, webassign.net/hprecalc/6-5-18.gif, and ... | |
| help. | 1/21/2009 |
| Q: I need to know how to do this problem. I don't have examples in my textbook. What is the period of ... A: As with the cos(t) function, the period is 2pi with 0's every pi. It is 1 at pi and every period ... | |
| help. | 1/21/2009 |
| Q: I need to know how to do this problem. I don't have examples in my textbook. Use the graph of the ... A: Remember what the cos(t) curve looks like. It starts at cos(0) 0 1 with slope 0. It slides down to ... | |
| Largest revenue | 1/20/2009 |
| Q: This question is a 3 part question and i am having difficulties with the third part. The question ... A: A was not done correctly, so the rest is not possible. I'll do (a) and take it from there. a) The ... | |
| Progression | 1/20/2009 |
| Q: I want a the solution for the following serious : N : non zero even positive integer Vo is the ... A: I will assume that N is always positive and even, since that is what I have been given. It can be ... | |
| Calculus | 1/20/2009 |
| Q: Apply implicit differentiation to find the max. and min. points on the graph of x^2 + 4y^2 - 2x - ... A: Then I will assume that dy/dx is the valid result. The only way that the fraction can be 0 is if the ... | |
| Calculus | 1/19/2009 |
| Q: Let f(x) = c/x + x^2. Determine all values of the constant c such that f(x) has a relative minimum ... A: I have found that no matter how large or small I make c, there is a maximum and a minimum. If I ... | |
| Calculus, Inverse Functions | 1/19/2009 |
| Q: If g(x) = 3 + x + e^x, find g^(-1)(4) * i was wondering how to find this using the steps for ... A: I don't believe that the inverse of a function with an x and an e^x can be written out. It's like ... | |
| calculus | 1/18/2009 |
| Q: Can you please help me with this question. K(x)=(2x^2+4x)e^-x I need the first, second derivatives, ... A: The first derivative involves the product rule with f(x) = (2x²+4x) and g(x) = e^(-x). The second ... | |
| Calculus | 1/17/2009 |
| Q: x f(x) f'(x) g(x) g'(x) 1 6 4 2 5 2 9 2 3 1 3 10 -4 4 2 4 -1 ... A: Since f(x) and g(x) are continuous functions. It is knowh that g(2) = 3 and g(3) = 4, so h(2) = ... | |
| calculus | 1/15/2009 |
| Q: X^2/3 (x-9) A: I would guess that since this is in calculus, it is suppose to be integrated. Multiply it out, ... | |
| problem | 1/13/2009 |
| Q: Write the expression as a single real number. Do not use decimal approximations. A) ... A: You need to know the sin() and cos() of 30° and 60°. 30° is π/6 radians and 60° is π/3 ... | |
| math | 1/13/2009 |
| Q: NEED BY TODAY PLEASE!!! A wheel in a large machine is 14 feet in diameter and rotates at 1490 rpm. ... A: (b) Sorry about that one, I started with a 14π, but then left out the π when I stated it ... | |
| math | 1/13/2009 |
| Q: NEED BY TODAY PLEASE!!! A circular saw blade has an angular speed of 19 radians per minute. (a) ... A: (a) There are 19 rad/min and 1 rev/2π rad, so multiply and you get 19/(2π) rev/min = ... | |
| math | 1/13/2009 |
| Q: NEED BY TODAY PLEASE!!! A wheel in a large machine is 14 feet in diameter and rotates at 1490 rpm. ... A: (a) There are 2π radians in a circle. The wheel rotates at 1490 rev/min. Multiply by 2π ... | |
| Pre calculus help | 1/12/2009 |
| Q: How do I solve: sec^2 x + tan x = 1 given that 0 degrees </= x < 360 degrees? I know that for tan x ... A: I answered this one just a minute ago, but here's another note. If tan(x) = 1, then x = 45° is ... | |
| Pre calculus help | 1/12/2009 |
| Q: How do I solve: sec^2 X + tan X = 1 given that 0 degrees </= X < 360 degrees? I do not understand ... A: The first thing I always do is convert sec²(x) + tan(x) = 1 to sin(x) and cos(x). It is known that ... | |
| Dimension Applications of Derivatives | 1/11/2009 |
| Q: Find the dimensions of the largest open-top storage bin with a square base and vertical sides that ... A: We've got to assume something, so lets assume that the base has width B and the height is H. The ... | |
| u-substitution in trigonmetric equations involving sin, cos, and tan | 1/11/2009 |
| Q: I have been struggling a bit in my trig class trying to understand u-substitution. An example of ... A: We know that sin(Θ) = 1/2, so you're right in saying that Θ=π/6. If you know what the ... | |
| AP Calculus | 1/9/2009 |
| Q: Let f be the function defined by f(x)=(x^3)+a(x^2)+bx+c and having the following properties. (i) The ... A: (i) A point of inflection is where f"(x) has the value 0. f"(x) = 6x + 2a. For the point (0,-2) to ... | |
| Inverse Functions | 1/9/2009 |
| Q: I'm having trouble solving 2 kinds of inverse functions, can you help me to approach this kind of ... A: Take y = (x+3)/(x+8). Multiply by x+8, giving xy + 8y = x + 3 Add -8y-x to both sides, giving xy-x ... | |
| calculus - related rates | 1/9/2009 |
| Q: A candy company needs a custom box for their truffles. The box they’ve chosen is in the shape of a ... A: This is only an estimate to the change in volume assuiming the change is linear, but the change is ... | |
| Applied Maximum | 1/9/2009 |
| Q: I have a problem here which asks me to find the dimensions of the right-circular cylinder of ... A: Sorry I missed that. That is the right formula for the surface area (top, bottom, and side) of a ... | |
| calculus - related rates | 1/8/2009 |
| Q: A candy company needs a custom box for their truffles. The box they’ve chosen is in the shape of a ... A: from [1], after looking at it, I would divide it into terms. We would get y = r + V/(πr²) - ... | |
| calculus - related rates | 1/8/2009 |
| Q: A candy company needs a custom box for their truffles. The box they’ve chosen is in the shape of a ... A: You might have got this part, but just for review: ... | |
| Applied Maximum | 1/8/2009 |
| Q: I have a problem here which asks me to find the dimensions of the right-circular cylinder of ... A: Geometry and algebra don't seem like they can solve it as easily as calculus. The height of the ... | |
| Related Rates | 1/7/2009 |
| Q: A balloon is being filled with helium at the rate of 4ft^3/min. The rate, s square feet per minute, ... A: We will assume the balloon is spherical. The volume is V(r) = 4πr^3/3, which says that r^3 = ... | |
| Calculus | 1/6/2009 |
| Q: Let f be the function defined by f(x)=3x^2-4-x^3/2 Find the exact x coordinates of any pooint where ... A: 1. First, any line parallel to y=9x-8 must have slope 9 since that is the slope of the line. That ... | |
| Pre calculus help | 1/5/2009 |
| Q: How do I develop the identity for cos 2A using the identity for cos (A+B)? Thanks very much for your ... A: Use the formula for cos(A+B). Let B=A so now you can replace all the B's in the formula with an A. ... | |
| About multiple integrals | 1/3/2009 |
| Q: I am doing B.TECH.IT in an engineering college , i find it difficult to solve multiple integrals ... A: The way to do multiple integrals is to treat all of the other variables as constants. For example, ... | |
| related rates- Thanks for your help!! | 1/2/2009 |
| Q: Let V be the volume of a circular cylinder having a height h and a radius r, and assume h and r vary ... A: To do this, three equations are needed: The volume of a cyllinder, the power rule, and product rule. ... | |
| calculus question | 1/2/2009 |
| Q: i have couple so if can answer which ever one you like(hope you answer all of them though lol) ... A: I know the feeling - I took algebra in 8th 1. The length of an are is ⌠ ⌡ [1 + ... | |
| tangency | 12/31/2008 |
| Q: Please, 1. The tangent point between g(x)=ax^2+bx+c and f(x)=mx+n is x1 resp y1. What's the slope ... A: 1. The slope of the tangent line is the same as g'(x). This would mean that m would have to be ... | |
| calculus related rates | 12/31/2008 |
| Q: The surface area of a cube is increasing at a rate of 50 square centimeters per second. How fast, ... A: We need to know the current size of the cube. It is known that the surface area is A(s) = 6s², ... | |
| calculus related rates | 12/31/2008 |
| Q: A conveyer belt deposits sand into a conical pile at a rate of 36 cubic feet per minute. If the ... A: The formula for the volume of a cylinder is πr²h where r is the radius and h is the height. ... | |
| derivatives | 12/31/2008 |
| Q: If f(x)=3x^2-5x, find f'(2) and use it to find an equation of the tangent line to the parabola ... A: The slope and the derivative are the same thing. The derivatve of ax^n is anx^(n-1); ex: f(x)=4x², ... | |
| Calculus Related Rates | 12/30/2008 |
| Q: Hey, The radius of a spherical ball is decreasing at a constant rate of 3 cm per second. I don't ... A: We know that the volume of a sphere is 4πr^3/3. Here, r is 5 cm. so the volume is 500π/3. ... | |
| Related Rates | 12/30/2008 |
| Q: Two trucks start from the same point. One tuck travels due east at a rate of 50 mph and the other ... A: In 1.5 hours, the first truck would be 50*1.5=75 miles east. In 1.5 hours, the second truck would ... | |
| Pre calculus help- word problem | 12/19/2008 |
| Q: If p pods could create 7 seedlings in 120 minutes, how many minutes would it take 3 more pods to ... A: If p pods (a variable P) could create 7 seedlings (a variable S) in 120 minutes (a time T), how many ... | |
| Calculus | 12/18/2008 |
| Q: Hay, I hope you can help me. Let F(x) be the function defined below: [x^2 -4xk+3h , x>or=4 ... A: Is this suppose to be F(x) = 1.5kx^3 - 3xh for x≤-2, F(x) = k for -2≤x≤4, and ... | |
| Vector Proof | 12/17/2008 |
| Q: Give a vector proof that the midpoints of the sides of a square are the vertices of a square. ... A: A point proof comes to mind first, so I'll start with that. x-y coordinates --------------- A graph ... | |
| Vertical Asymptote | 12/16/2008 |
| Q: I am tryng to find the vertical asymptote of the following equation but I am confused by a negative ... A: To find the vertical assymptote, that would be where the denominator is 0. Looking at the problem, ... | |
| calculus integrals | 12/12/2008 |
| Q: Can you please give me an example of an integral of polynomial? A: To integrate any polynomial, for each term, raise the power of x by one and divide by the new ... | |
| differentiation maybe. | 12/11/2008 |
| Q: A population of bacteria is changing at a rate of dp/dt = 3000/(1+.25t) A) Determine the rate of ... A: A) No maybe's to it. The rate of change is the value of the derivative. Find the derivative of ... | |
| Rectangular Pen Problem | 12/10/2008 |
| Q: A rectangular pen is built against a wall so that only three sides will require fencing. If f fet ... A: For the variables, y is the length, x is the width, f is the total fencing, and A is the area. The ... | |
| Fibonacci convergence | 12/10/2008 |
| Q: I was given a problem by my professor to be graded as a quiz. It is to find the exact expression ... A: Note that in this equation lim (n->∞) F(n+1)/F(n) = 1 + lim (n->∞) F(n-1)/F(n), we know ... | |
| Acceleration or Velocity | 12/10/2008 |
| Q: Mary has been practicing to race in a 10 kilometer race. She would run every day. At the beginning ... A: R(d) can't be negative since R(d) is the distance she travelled. R"(d) is the rate of change in ... | |
| Calculus | 12/9/2008 |
| Q: I really need help on this question if you dont mind. A particle starts at time t=0 and moves along ... A: A) correct B) correct C) f(t)=(1-t)², g(t)=8t-11, f'(t)=2(t-1), g'(t)=8 fg' + gf' = (1-t)²(8) + ... | |
| Sinusoidal Functions | 12/8/2008 |
| Q: Hey Sir, I need like serious help with this question. Could you please tell the equation how to ... A: When the function is sinusoidal, that means we have a cos(x) function involved. The minimum should ... | |
| Calculus | 12/8/2008 |
| Q: I really need help on this question if you dont mind. A particle starts at time t=0 and moves along ... A: Now the problem was given as 'A particle starts at time t=0 and moves along the x-axis so that ... | |
| Double Integral question | 12/8/2008 |
| Q: Here is my problem: Calculus: evaluate ∫(INT 9 to 8) ∫(INT 7y to 5y) (7/x) dx dy I ... A: When we are integrating 7/x, the 7 can be put out front so we are only integrating 1/x. From ... | |
| Volume of Revolution | 12/7/2008 |
| Q: The function f is denoted by f(x)= (ln(x))/(x^3), x >or= 1. The region enclosed by the x-axis, the ... A: Just like the area of a circle is πr², the volume of a rotation is given by the integrating the ... | |
| Trigonometry | 12/7/2008 |
| Q: I am struggling with problem, could you tell me if I am correct or if there is more work, or what I ... A: I'm not sure where the identity came from that was used, but the correct identity for tan(α/2) ... | |
| epsilon delta | 12/6/2008 |
| Q: For the limit below, find values of δ that correspond to the ε values. lim(x->3)(5x-11)=4 ... A: The function is 5x-11 and the result is 4. To see how big δ needs to be, take the equation ... | |
| Calculus - Deman Functions | 12/6/2008 |
| Q: i really need some help on this calculus problem. It would be greatly appreciated if you can help ... A: n=number of rebate Price: (360 - 12n) Number sold: (1950 + 120n) a) pirce = number * price; ... | |
| projectiles | 12/6/2008 |
| Q: I have been asked to find the angle that gives the maximum length of arc in ( horizontal) ... A: Take v as the velocity and we have the distance is cos(α)vt. The speed at which the projectile ... | |
| Inv Trig Differentiation | 12/6/2008 |
| Q: Trying to differentiate Arcsin (sqrt (1-x )). Can you help me? Do I need all the square roots? I ... A: Here is a note: dy/dx is really a fraction. If y=x², dy/dx = 2x dx, so dy = 2x dx. If y=4x^3, dy/dx ... | |
| calculus | 12/5/2008 |
| Q: the fluid H cm in a vessal at the time t is given by H=16+4t+2t^2-t^3/16 what is the rate which ... A: The rate of change is the value of the derivative. The derivative is found by applying d(x^n)/dx = ... | |
| Trigonometric reduction | 12/5/2008 |
| Q: I am trying to figure out how to use the Reduction Identity to write the following in terms of sine ... A: These are the equations that will be used [A] sin²(y) + cos²(y) = 1, [B] sin(2x) = 2sin(x)cos(x), ... | |
| DeMoivre's theorem | 12/3/2008 |
| Q: I need to use DeMoivre's theorem to find what (1-i)^3 is, using rectangular coordinates. I know it ... A: DeMoivre's theorem is a way to convert from polar to rectangular coordinates. When a number in ... | |
| chemistry | 12/2/2008 |
| Q: Hydrazine, N2H4 and hydrogen peroxide, H2O2, have been used as rocket propellants. They react ... A: The molecular weights of one mole of each of the following is given: 34.01 grams for Hydrogen ... | |
| Calculus | 12/2/2008 |
| Q: Building a new gym: To expand upon the newly expanded gym, the athletics department has found alumni ... A: The gym is x feet long, y feet wide, and therefore y/2 feet tall since the top is circular. The ... | |
| Derivatives | 12/2/2008 |
| Q: i just wanted to know that what is derivative?i'm mba student,i have to deal with derivatives in ... A: I don't know how the equations fit, but I can say that derivatives are not that hard when speaking ... | |
| rates of change | 12/1/2008 |
| Q: A man who is 6 feet tall is walking at a range of 84 ft/min toward a street lamp that is 20 feet ... A: I believe the problem is this: A man is 6 feet tall, he is moving at 84 ft/min, the lamp is 20 ... | |
| finding max area | 11/30/2008 |
| Q: A rectangular pigpen is to be built against a wall so that only 3 sides will require fencing. If 'p' ... A: Take s as one side and p-s as the other side. The total area would be s(p-s) where p is a constant. ... | |
| calculus | 11/30/2008 |
| Q: A point moves along the curve y=x^2 + 1 in such a way that when x=4, the x coordinate is increasing ... A: The rate of change is the first derivative, so we get dy = 2x dx. We know that x is 4 and dx is 5, ... | |
| Min/Max problem | 11/29/2008 |
| Q: Find the point(s) on the hyperbola x²-y²=4 that is closest to the point (1,3). A: Take (x1,y1) to be a point on the curve x²-y²=4. The distance is √[(x-1)²+(y-3)²]. We can look ... | |
| Volume of object by calculus | 11/29/2008 |
| Q: I need to find the volume of a sweet potato via calculus. I would appreciate any ideas, because I've ... A: There are two ways to do this, depending on whether this is for (1) math or for (2) a recipe. (1) ... | |
| Calculus question! | 11/29/2008 |
| Q: Given the function f(x)=e^-x^2 (a). Find the derivative of f (b). Find the critical values (c). ... A: (a) The derivative of e^g(x) is e^g(x) * g'(x). (b) The critical values are where the first and ... | |
| Find the asymptotes and intercepts of the function and graph it | 11/28/2008 |
| Q: f(x)=(2x squared +7)/(x squared +x-6) I have no idea how to do this. A: The assymptotes usually occur where the denominator is zero. Set x² + x - 6 = 0 and solve for x. It ... | |
| calc. | 11/25/2008 |
| Q: Let f be the functon defined by f(x)= 7-15x+9x^2-x63 1 find the zeros of f 2 write the eqation of ... A: It is probably save to assume that the problem is f(x)= 7-15x+9x^2-x^3 (that 6 should really be a ... | |
| App for generating calculation results & table? | 11/24/2008 |
| Q: What free app could I use to automatically calculate [& hopefully generate a table] for the ... A: I would do it in Excel. In A1, put 6. In B1, put 13. In C1, put 20. Now I would leave row 2 ... | |
| Increasing/decreasing intervals | 11/24/2008 |
| Q: I understand increasing and decreasing intervals for a function using the first derivative. Why are ... A: I went out and found the answer. It was in http://www.math.hmc.edu/calculus/tutorials/secondderiv/ ... | |
| algebraic inequalities | 11/24/2008 |
| Q: Two graphic artists are working on a 3D game project. One artist works 3 hours more than his ... A: Lets call the time that each of the graphic artists works A and B. They may work on a 3D game ... | |
| inequalities | 11/24/2008 |
| Q: Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she ... A: Jenny, garden, flowers. Triangular area, different lengths for each side. [1] B=A-5, [2] C=A+4, and ... | |
| find the dimensions for the building that minimize the total cost of the building. | 11/23/2008 |
| Q: the volume of the dorm must be exactly 225,000 cubic feet, which is one cubic foot for each sprout ... A: Foundation: #30/ft²; sides: $20/ft²; and roofing: $15/ft². The dimensions of the building are L, W, ... | |
| calculus- optimization | 11/22/2008 |
| Q: A pipeline must be laid from point a to point b. Point b is located 31 miles east and 40 miles north ... A: Points: A,B Point B: 31 east, 40 north of point A Horizontally: 21 east water, 15 east land Cost: x ... | |
| Algebra Help | 11/21/2008 |
| Q: I am working on the word problem Barbanegra the pirate: ... A: Directions are: He is at 0,0 and the other men is at 8 east ,6 south, ONe man is at 6 east, 2 north, ... | |
| Calculus | 11/21/2008 |
| Q: Find the greatest volume that a right circular cylinder can have if it is inscribed in a sphere of ... A: The volume of a right circular cylinder is πr²h where h is the height and r is the radius ... | |
| CALCULUS | 11/20/2008 |
| Q: How do I find the derivative of: f(x)=5-|x-5| A: You have to divide it into two functions. f(x)=5(x-5) for x≥5 and f(x)=5(-x+5)=5(5-x) for ... | |
| Increasing/decreasing intervals | 11/20/2008 |
| Q: I understand increasing and decreasing intervals for a function using the first derivative. Why are ... A: Do you mean (180°,360°) not [180°,360°]? Well, if 180° is chosen, it is on the edge of the ... | |
| Increasing/decreasing intervals | 11/20/2008 |
| Q: I understand increasing and decreasing intervals for a function using the first derivative. Why are ... A: You're right when you say that it doesn't make sence that a function can be increasing and ... | |
| trigonometry analysis | 11/19/2008 |
| Q: How would you find the six trig funtion for an angel of 34 degrees? I'm not quite sure how you would ... A: The first three trig functions are sin, cos, and tan. They are sine, cosine, and tangent. The ... | |
| Calculus realted rate | 11/19/2008 |
| Q: A man is walking on a bridge that is 20 ft above a river, as a boat passes directly under the center ... A: Boat: directly below at 10ft/s, so x=0 and dx/dt = 10 (x is how far up the river I can find the ... | |
| calculus, Illumination problem | 11/19/2008 |
| Q: Consider a horizontal road illuminated by two lights, where Pi is the illumination power of Li, the ... A: The light from one lamp is P1/√(H1²+x1²). The light power from the other lamp is ... | |
| Calculus- Optimization | 11/18/2008 |
| Q: An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to ... A: Refinery: 1 km up river Pipleline from refinery to other bank, 7km away. Cost for land is ... | |
| Minimizing Cost of a Airplane Hangar | 11/18/2008 |
| Q: hopefully you can help me out with this question! The volume of the dorm must be excatly 225,00 ... A: If L is thelength and W is the width, I can say the area A of the floor is A=LW and it's cost is ... | |
| calculus | 11/18/2008 |
| Q: let f be the function given bbby f(x)= x^3-5x^2+3x+k where k is a constant 1- on what intervalls is ... A: 1- The function is increasing wherever the derivative is positive. 2- The function is concave ... | |
| =) | 11/17/2008 |
| Q: y= ((3x^2-1)^5/(x^2+1)^4) a) find y' by the quotient rule (do not simplify) b) simply y' completely A: a) Let f(x) = (3x²-1)^5 and g(x) = (x²+1)^4. It is known that f'(x) = 5(3x²-1)^4(6x), since 6x is ... | |
| I don't get it | 11/17/2008 |
| Q: find: lim x-> 0 (sin^2(5x)/x^2) A: Note that this is the same as [lim (x->0) (sin(5x)/x) ]^2. Once this has been done, note that the ... | |
| So confused | 11/17/2008 |
| Q: f(x) = (x^2-x+3/cube rt(x)) a) find f'(x) b) write f'(x) in factored form c) find all x where x has ... A: The function is given by 1 or 2 choices. 1) Using basic mathematic principals, this function could ... | |
| Horizontal and Vertical Asymptote | 11/17/2008 |
| Q: all i am asked to do is find all Horizontal and Vertical Asymptotes but the square root in the ... A: Is this suppose to be f(x) = √(5x^6-5) / (4x^3-11x)? To find the horizontal assymptotes, look ... | |
| AP Calculus BC | 11/16/2008 |
| Q: Determine whether Means Value Theorem can be applied to f on the closed interval [a,b], if so, find ... A: The function should be multiplied our to give f(x) = x^3 - x² - 2x. Each of these (x^3, -x², and ... | |
| Maximum profit | 11/16/2008 |
| Q: A merchant plans to sell two models of compact disc players at costs of $125 and $250. The $125 ... A: Two costs: $125, $250 Profits: $125 -> $30 and $250 -> $35. Total demand -> won't exceed 250 units. ... | |
| drawing and plotting graph | 11/15/2008 |
| Q: Sir I am very confused that how to shade graph of inequalities?In my book the shaded part is a ... A: The best way I've found to do it starts with drawing the line x - 2y = 6. This would be better if ... | |
| calculus | 11/14/2008 |
| Q: how to integrate >> int[tan(x^2)]dx?? A: We know that tan(x)=sin(x)/cos(x), so tan²(x)=sin²(x)/cos(x)². Using this function, let u=sin(x), ... | |
| PreCalc Proof | 11/14/2008 |
| Q: I need a bit of help on starting this proof on my Honors Precalc HW. I have to prove that it is an ... A: Far side a, near side b, hypoteneuse c (1 + a/c + b/c)/(1 + a/c - b/c) = (1 + b/c)/(a/c) Put ... | |
| calc 3 | 11/13/2008 |
| Q: A particle moves in space along a curve with representation r(t)=t(i)+2sin(t)j+3cos(t)k for t >=0 * ... A: Notes ----- The hats aren't necessary if you change 'representation r(t)' to 'representation of the ... | |
| Optimization | 11/13/2008 |
| Q: Suppose that you go to a lake on a nice summer day. Someone throws a ball into the water and it ... A: Since the horizontal distance is L, the distance in water from the closest point on the land is d, ... | |
| Optimization in Calculus | 11/13/2008 |
| Q: You are a lifeguard and are standing on the shore of a calm lake. You see a person in need of help ... A: IF this is the case, run along the short until you feel like jumping and don't take time to compute ... | |
| Related rates with Triangles | 11/13/2008 |
| Q: A ladder 25 feet long is leaning against the wall of the house. The base of the ladder is pulled ... A: When the ladder is 7 feet from the wall, the height is known to be 25² - 7² = 625 - 49 = 576, which ... | |
| Proofs | 11/11/2008 |
| Q: Scott, I typed in the question poorly. Here it is again. Prove that 81 divides (10^(n+1) -9n -10) ... A: It's a pity I can't line up numbers. The numbers in this letter are lined up in columns on my end. ... | |
| Mean Value Theorem | 11/11/2008 |
| Q: I am stuck on a particular problem. I know what the mean value theorem is but I have no idea where ... A: The Mean Value Theorem says that if C is in between f(a) and f(b), and D=b-a, then integral(a to ... | |
| help | 11/11/2008 |
| Q: in a exponential growth and decay modeling data formula how do you calculate ... A: If the inner hourse is in question, the radius is 6 feet. That would mean the distance he has to ... | |
| Proofs | 11/10/2008 |
| Q: Scott, I typed in the question poorly. Here it is again. Prove that 81 divides (10^(n+1) -9n -10) ... A: N Answer Result 1 81 1 2 972 12 3 9963 123 4 99954 1234 5 999945 12345 6 9999936 123456 Here you ... | |
| calculus-finding 2nd derivative of a rational function | 11/9/2008 |
| Q: how to find the 1st and 2nd derivative of (x+1)^2/ 1+x^2 inflection points and concavity A: This looks like (x+1)²/(1+x²). It is a quotient rule with f(x)=(x+1)² and g(x)=1+x², therefore ... | |
| equation of normal line | 11/8/2008 |
| Q: I have one question about the equation of the normal line: 1) Let (3+tan(x))/(sin(x)). Write the ... A: The equation to the line must have the same slope where it contacts the curve. The slope of where ... | |
| Solving the matrix - reg | 11/7/2008 |
| Q: Attached the image of matrix equation. I have to develop computer program for that.Could you please ... A: I'm not sure this is what you want, but to multiply matrices together, multiply each row of the ... | |
| Derivative word problem | 11/7/2008 |
| Q: 1. f(x)=sqrt(x-1) a) Draw a graphical representation of the method or process of finding ... A: (a) I don't yet have a scanner to scan this in, so I can't do (a). I can tell you it is similar to ... | |
| Proofs | 11/6/2008 |
| Q: Prove that 1+1/4+1/9+...1/n^2 <or= 2-1/n for every positive integer. A: There might be a more elegant way to solve the problem, but this one works. For n=1, we have 1 = 2 ... | |
| Solving the matrix - reg | 11/6/2008 |
| Q: Attached the image of matrix equation. I have to develop computer program for that.Could you please ... A: I'm not sure what bias is, but I'll call it ß to go with α. The right hand side looks like a ... | |
| Closing off the First Quadrant | 11/5/2008 |
| Q: You are planning to close off a corner of the first quadrant with a line segment 20 units long ... A: Take some point x on the x-axis. This would make the point on the y-axis 20-x. The triangle area ... | |
| Calculus 1 | 11/4/2008 |
| Q: an object is thrown upwards from the ground w/an initial velocity of 128 ft/sec use: ... A: a) We are given v0 = 128 (positive, since it is upward) and s0 = 0 (since it is from the ground). ... | |
| f(4) | 11/4/2008 |
| Q: Suppose f(x) is a differentiable function for all real numbers x which also satisfies: f '(4) = 0, ... A: WHen they say that f'(4) is 0, we already know an approximate value for f(x). See, we know that the ... | |
| Partial Fractions | 11/4/2008 |
| Q: Hey, I'm a first year Natural Science undergrad at Cambridge University, and I'm having an absolute ... A: The two fractions are of the form A/Y and B/(K-Y). The way to find what they are is to set ... | |
| Calculus curve sketching | 11/3/2008 |
| Q: I was given the problem y=x times the square root of (3-x) and I need to find the relative max and ... A: The inflection points are the points that are between where the curve is concave up and concave ... | |
| Calculus | 11/3/2008 |
| Q: A landscaper has 150 feet of privacy fencing to use to fence a yard. One of the short sides of the ... A: Call the width of the yard W. He will need 2W feet to fence both sides of the yare. This will ... | |
| Calculus curve sketching | 11/3/2008 |
| Q: I was given the problem y=x times the square root of (3-x) and I need to find the relative max and ... A: Is the problem x√(3-x)? The derivative is √(3-x) - x/(2√(3-x)). I believe that's ... | |
| Calculus and bugs | 11/2/2008 |
| Q: I can't see how to use calc for the following problem, I can do it with Geometry though, please ... A: Consider unfolding the room. The bugs is in the upper corner of one square and where he is walking ... | |
| Integration | 10/31/2008 |
| Q: I am stuck on the following integral: sqrt(a - bx^2)dx Actually, i need to solve the following ... A: Factor out √b, so the problem reduces to √b√(a/b - x²). Let the constant a/b be ... | |
| differential equations and propagating error | 10/31/2008 |
| Q: The measurements of the base and altitude of a triangle are found to be 32 and 54 centimeters, ... A: The area of a triangle is bh/2 where b is the base and h is the height. What we have is ... | |
| puzzle | 10/31/2008 |
| Q: 12 wooden cubes, all different size and color. the largest cube is 12cm on a scale, the next is 11cm ... A: Lets label the volume of each of the colors red, blue, orange, yellow, green, purple, silver, white, ... | |
| max/min | 10/26/2008 |
| Q: A triangle is formed by a line through (4,1) and the two coordinate axes. a) Is there a minimal area ... A: The line passing through (4,1) has the equation y-1=m(x-4) and sope m. To find the y intercept, ... | |
| calculus 2 | 10/26/2008 |
| Q: Water in a bowl evaporates at a rate proportional to the area of the surface of the water. In other ... A: The amount of water decrease at a rate the is proportionate to the surface area. The volume of ... | |
| Maclaurin Series | 10/26/2008 |
| Q: What would be the Maclaurin series for (1-cosx)/(x^2),(x≠0) and what would be the easiest way ... A: A Maclaurin Series is a Taylor's Series with the expansion being about 0. It is given in the top of ... | |
| Integration -- acceleration, velocity | 10/25/2008 |
| Q: A speeding motorcyclist sees his way blocked by a wagon some distance 's' ahead and slams on his ... A: Distance: s Accleration: a (a negative number) Wagon speed: v (in same direction as motorcycle) ... | |
| max/min | 10/22/2008 |
| Q: need some help minimizing this equation... (58+Rpi)(500000/pi)(r^-1)+19*pi*r^2 where R is a ... A: The function is (58+Rπ)(500000/π)(1/r)+19*pi*r² and we are using r as the variable. ... | |
| Combinations Pick 5 in set of 12 | 10/20/2008 |
| Q: I am a jazz musician searching for a method to eliminate contrafacts in a particular subset of ... A: I have never heard of a hemitonic or pentatonic scale. However, lets consider being in the key of ... | |
| Pre-Calculus | 10/20/2008 |
| Q: What is an apparent maximum? A: I believe it is also called a local maximum. It is where the first derivative is 0 and the graph is ... | |
| derivatives | 10/20/2008 |
| Q: . I'm taking calculus my senior year of high school and it's basically torture. I don't understand ... A: The derivative is csc(x)cot(x) - cos(x). Note that cot(x) = cos(x)/sin(x). This makes the formulate ... | |
| Fidn the derivative | 10/18/2008 |
| Q: Find the derivative: f (x) = ln ((x2√4x + 1) / (x3 + 5)3) A: I will assume the function is f(x) = ln((x²√(4x) + 1) / (x^3 + 5)^3). The derivative is of ... | |
| limits | 10/18/2008 |
| Q: what is the limit of this (x*x-64)/(x-2) when limit,x --> 2 A: The top goes to -60 and the bottom goes to 0, so the limit is ∞. If the problem was ... | |
| help | 10/17/2008 |
| Q: Draw the graph of y=2^x over the interval -1<_x<_3. Will this graph ever intersect the x-axis/ ... A: A positive number to any power is never zero, so it can't cross the axis anywhwere (including in ... | |
| Calculus - Find the limit | 10/16/2008 |
| Q: This one is kicking my butt, I feel really dumb. How do I find the the limit. lim ∑ (1 + ... A: I don't think it will kick too hard... Over i is the sum from 1 to ∞. The summation can be ... | |
| Math | 10/16/2008 |
| Q: In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were ... A: C=new car R=new refrigerator W=new washer N=consumers n=intersection u=union N=75 C=12 R=18 W=24 ... | |
| Linear vs. Angular Speed | 10/16/2008 |
| Q: a patrol car is parked 50 feet from a long warehouse. the revolving light on top of the car turns ... A: Partol car: 50 ft from wall Light on top of car: revolving at 30 rev/min, which is 2π ... | |
| Calculus | 10/15/2008 |
| Q: How would I definite integral that represents the area of the region enclosed by y = 4x – x2 and the ... A: I will assume the question is to be read as, 'How do I define the integral that represents the area ... | |
| calculuse | 10/15/2008 |
| Q: good morning . can you help me please in solving the following equation : sin (2x ) + tan ( x ) = ... A: Try and put in sin(2x)=2sin(x)cos(x). Once you have done this, it can be solved by converting ... | |
| Volume of a Rotation (Integration) | 10/15/2008 |
| Q: An instructor told me if I am bored in calc 2 to try volume of rotation about something with a ... A: The endpoint are where x²=2x (there are two solutions). The radius of rotation is y=x²-2x as long as ... | |
| Math | 10/15/2008 |
| Q: How do I write the following in roster form: Set J is the set of natural numbers between one and ... A: (a) That's what the first statement says is the number with refrigerators (yeah, sometimes math ... | |
| Calculus Issue | 10/14/2008 |
| Q: I recently had my first calculus exam. It was primarily a test on review material. In a study ... A: One way to see what the limit is: Look at the Taylor's theorem for cos(x). The Taylor's theorem ... | |
| Solids of Revolution | 10/13/2008 |
| Q: I can calculate the volume of a solid if it is revolved around the x or y axis, but if I were asked ... A: The formula needs to be converted so that it looks like it is being revolved around an axis. For ... | |
| Trig Limit solving with a square root | 10/12/2008 |
| Q: and I understand most of the work, but I am having trouble with solving for a limit using only the ... A: If we multiply the top and the bottom of the fraction by √(1+3x) + 1, we get (x(√(1+3x) ... | |
| Calculus Derivative Using The Technique of Logarithmic Differentation | 10/11/2008 |
| Q: Find the derivative of Using the technique of logarithmic differentation y = {[(x - 3)^4 (x^2 + 1)] ... A: Isn't logarithimic differentiation where you say ln(y) = ln({[(x - 3)^4 (x^2 + 1)] / (2x + ... | |
| Maximize | 10/11/2008 |
| Q: You did a great job helping me with a previous question, hopefully you can do one more! Thanks! *A ... A: Let T = number of trees and let A = nummber of apples per tree. Let x be the additional trees that ... | |
| calculus | 10/11/2008 |
| Q: The question is Y^(3/4) = 2x+2. I would like to solve for Y (Leave Y by itself on the left hand ... A: When you have an equation that has y to a power n, just take both sides to 1/n. Here, you take ... | |
| Vectors in 3D Type Questions | 10/11/2008 |
| Q: I'm having a little difficulty with doing three of these math questions and since it's the school ... A: In my first response, I only answer question 1. I then looked back and remembered there were two ... | |
| Optimization | 10/10/2008 |
| Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its ... A: The volume would be hb² where h is the height and b is the base. Notice that 2b² + 4bh = 253.5, so h ... | |
| optimization problems | 10/9/2008 |
| Q: I'm sure this is easy but I am terrible with calculus. Find the minimum of Q = x2(squared) + ... A: Take the function and substitute in 6-x for y. This will give you a function of x only. There is ... | |
| A certain calculus student hit Mr. Leacher | 10/8/2008 |
| Q: A certain calculus student hit Mr. Leacher in the head with a snowball. If the snowball is melting ... A: To evaluate 10/4*π*(2)^2 , 10/4=2.5, π=3.1416 (rounded to four places), and 2^2=4. Take ... | |
| Good help in past,could you help with another | 10/7/2008 |
| Q: A conical tank is 14 ft. across the top and 12 ft. deep. Water is flowing in at the rate of 30 cu. ... A: Since it's flowing in at 30 and out at 20, the net flow is in at 30-20=V. The surface area ... | |
| maclaurin's series expansion | 10/7/2008 |
| Q: in the maclaurin's series expansion of tan-1(x): tan-1(x)=x – x3/3 +x5/5-.....; the expansion is ... A: Because if x is greater than 1, there series won't hold. For example, suppose x were 2. It would b ... | |
| Indefinite Integral | 10/6/2008 |
| Q: What is the indefinite integral of 1/(1+e^(.2t)) A: 0.2t is t/5 and will be written as such. If u=e^(t/5), du = e^(t/5)/5 dt. Looking at the integral, ... | |
| pre-calc | 10/4/2008 |
| Q: Hey there. My professor gave us a huge 50 problem assignment and I am stuck on these few remaining. ... A: 1. Consider the functions f(x)=3rd√(x-1) g(x)=x^3 +1 Find each of the following, if possible. ... | |
| Calc - Find Eq of Tangent Line | 10/3/2008 |
| Q: x^2 + xy + y^2 = 1 a) find all pts which the tangent line is horizontal (m=0) b) find all pts in ... A: To take the derivative just as the problems written. The second term is a product rule and the last ... | |
| calculus | 10/2/2008 |
| Q: A 10m ladder is leaning against a vertical wall and its base is slipping away from the wall at a ... A: Now for some reason I prefer dx/dt and dy/dt in place of x’ and y’. A 10m ladder is leaning against ... | |
| Help with Calculs word problem | 10/2/2008 |
| Q: Welbilt Design and Construction has recently begun the construction of a series of carefully ... A: If the material is 19" wide, we must put x inches in the base and (19-x)/2 in each side. I believe ... | |
| graphing and functions | 9/30/2008 |
| Q: Please help!! Create function below that is true for all of the following (I'm not sure how to show ... A: The value f(x0) is another way of saying the value of y when x is x0. Given this, we want y to be 3 ... | |
| Finding Continuity in 3D | 9/30/2008 |
| Q: Having a bit of trouble with this question.... Define f(0,0) in a way that extends f(x,y)= x^2 - ... A: It looks like the problem should be (x²-y²)/(x²+y²). This factors into (x+y)(x-y)/(x²+y²). If we ... | |
| Calculus | 9/22/2008 |
| Q: I have to Use Intermediate value theorem to prove sinx-x/2 =0 has a solution in the interval [1,2] A: According to //en.wikipedia.org/wiki/Intermediate_value_theorem , one way to express the ... | |
| Continously compound interest | 9/15/2008 |
| Q: Suppose that you discover in the attic an overdue library book on which you grandfather owed a fine ... A: If the interest rate is 0.05 and is compounded anually, take 1.05 to the number of years and ... | |
| abslute value correction | 9/15/2008 |
| Q: In my previous question I said the book said 7 I was wrong I was looking under the wrong section the ... A: Well, I only answer questions one at a time and I already answered the previous one. Yes, -1 is the ... | |
| Absolute value limit | 9/15/2008 |
| Q: |X| / X When the limit goes to 0 from the left. The answer in the book says 7 but how did they get ... A: Since it is approaching from the left, X is negatvie. This means the function is -X/X, which is ... | |
| rotating about an axis and finding the area | 9/14/2008 |
| Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/4 x^2 - ... A: They are different because they are entirely different functions. To rotate a function around the y ... | |
| Pre Cal | 9/14/2008 |
| Q: The length of a rectangle is 7 cm greater than its width and a diagonal of the restangle is 2cm ... A: Let length of the rectangle is L, the width is W, and the diagonal is D. The equations that we have ... | |
| Related Rates | 9/11/2008 |
| Q: a waterskier skis over the ramp that has a base of 15 ft. and a height of 4 ft. (it's a triangle) at ... A: The ramp's base is 15 and the height is 4. She is travelling at 30 ft/s. The height is 4 and the ... | |
| Related Rates | 9/11/2008 |
| Q: I really need help with thisThe volume of a cube is increasing at a rate of 10 cubic cm./min. How ... A: The size of the cube is 10 cm on each edge, to which I will say x=10 originally. We are interested ... | |
| mathematics | 9/11/2008 |
| Q: pleas i want a note on;(1) mean value theorem (2) curve sketching (3) cost function and (4) demand ... A: (1) The mean value theorem states that if a function is continuous on [a,b] then there is some point ... | |
| u-substitution problems! | 9/11/2008 |
| Q: I'm having some trouble with two problems and was hoping you could help me! The question says ... A: You are trying to find the antiderivative, or integrating the problems. This means that the first ... | |
| Asymptotes | 9/11/2008 |
| Q: Given the function of f(x), determine all asymptotes and explain or show why and where they occur. ... A: An assymptote is a line that is approached but never crossed. Start by factoring the equation. The ... | |
| Double Angel | 9/10/2008 |
| Q: Well.. I've never asked an online question before, but this is due by midnight and I really need ... A: Welcome to the land of PC service. Not only that, this service is free (that's unusual). If we are ... | |
| Calculus III | 9/9/2008 |
| Q: Consider the curve r(t)=(sin(t)cos(t))i + (sin(t)^2)j + cos(t)k a)Show that the curve lies on a ... A: a) To lie on a plane, any point must follow the equationx²+y²+z²=K. In this case, K=1. Square the ... | |
| Pre-Cal.-Evaluating a Difference Quotient. | 9/7/2008 |
| Q: For f(x)=4/x+1, find f(x)-f(15)/x-15 hi there, I saw in one of your past tutors who had a ... A: It looks like all you need to do is put 15 into the function and then put that into ... | |
| integrate e | 9/5/2008 |
| Q: How do I integrate e^(square root of x) with respect to x? Thank you. A: To do this requires a u substitution, addition of some expressions, and then a u-dv substitution. ... | |
| relativity | 9/3/2008 |
| Q: I do not know if you will understand. I am retired and amusing myself by studying relativity. I ... A: Let the space travelled by this bicyclist be s. His velocity is v=ds/dt. His acceleration is ... | |
| prove a theory by assumption | 9/3/2008 |
| Q: when I was at school, many years ago, we would prove mathematical theories by making an assumption ... A: You can use it when there is something that is known. For example, let's say you want to know 4²-6, ... | |
| relativity | 9/3/2008 |
| Q: I do not know if you will understand. I am retired and amusing myself by studying relativity. I ... A: 1. Acceleration is really d^2f/dt^2 where f(t) is the position function. 2. The number refers to ... | |
| Baccarat combinatorial analysis | 9/3/2008 |
| Q: How to use combinatorial analysis to calculate Baccarat probabilities? Baccarat is a casino game ... A: Since there are 8 decks of cards, that would mean that there are 32 of each card and 104 of each ... | |
| calculus | 9/1/2008 |
| Q: Find the limit: lim 1-sqrt(2x^2-1)/x-1 x->0 A: The answer seems to be a complex number since when x approaches 0, the √(2x²-1 approaches the ... | |
| Calculus Derivatives | 8/30/2008 |
| Q: If f(2) = 3 and the derivate of f(2) = 5, find an equation of a) the tangent line, and b) the ... A: We know a point (2,3)=(x0,y0) and the slope is 5=m, so use the point-slope form of the equation of a ... | |
| precal | 8/30/2008 |
| Q: a peice of wire 12 inches ong is to be usd to form a square and/or a circle. Determine a function ... A: In the square I will put 12-x units and in the circle I will put x. This will add up to 12. The ... | |
| precalulus homework help | 8/29/2008 |
| Q: a tour bus has 80 seats. experience shows that when a tour bus costs $300, all seats on the bus will ... A: The number of seats taken starts out as 80. For each $10 increase in price, two fewer seats would ... | |
| precal | 8/29/2008 |
| Q: a one mile race tack has two semicircular ends connected by straight lines. express the area ... A: To define the area of the track given r, we know that the sum of the two ends is πr². I will ... | |
| precal | 8/29/2008 |
| Q: a peice of wire 12 inches ong is to be usd to form a square and/or a circle. Determine a function ... A: If x units are in the circle, then 12-x units are in the square. The area of the square is s² where ... | |
| advanced calculus proof help | 8/28/2008 |
| Q: I need to show that: ||x -y||*||x +y|| ≤ ||x||² +||y||² I've tried many things and no luck, ... A: If is known that (x-y)(x+y)=x²-y²<=x²+y². There are only four choices to consider since for any x ... | |
| calculus | 8/27/2008 |
| Q: what will be the derivatives of these functions? a)r=sin(3pit/2)+cos(3pit/2) , ... A: what will be the derivatives of these functions? a)r=sin(3pit/2)+cos(3pit/2) I will assume that's ... | |
| multiplying polynomials | 8/27/2008 |
| Q: 2x(-3x+3)(-2x+6) when i multiply by 2x first i get 24x^4-96x^3+72x^2 when i multiply the ... A: There are two ways to multiply this problem. (2x(-3x+3))(-2x+6) or 2x((-3x+3)(-2x+6)). The first way ... | |
| Inverse of a function | 8/27/2008 |
| Q: my question is how do I find the inverse of f(x)=e^x/(1+9e^x)? A: Try taking the ln() of both sides. The left side in the ln(f(x)). The right side is the ... | |
| Calculus- Derivatives | 8/27/2008 |
| Q: I was wondering if you could explain what the dx/dy is and how to use it. And how would you find ... A: The derivative of (f(x))^n is n(f(x))^(n-1)f'(x). Here, f(x)=2x-7 and n is 3. At (0,36), we have ... | |
| Maxima minima using partial differentiation | 7/29/2008 |
| Q: For a function such as y = ax + bz that depend on 2 or more variables (2 in this case), why is ... A: The reason that this provides a solution is that the partial derivative in each variable is like if ... | |
| pre calculus | 7/29/2008 |
| Q: write tan(t) in terms of sin(t), given that (t) is in quadrant IV A: In quadrant IV, sin() is negative and cos() is positive. Since tan()=sin()/cos(), this would make ... | |
| QUES. on INTEGRTION BY PARTS | 7/28/2008 |
| Q: What is the integral of- sin sqrt(x)???...plzz..help me out mate..!!! thnxs a lott. A: It would seem like you could let u = √x, but then du = dx/(2√x), but √x is not in ... | |
| caluclus | 7/26/2008 |
| Q: how to find intercepts on graphs using cubics? A: There is no simple way to do this. Method 1: Take the derivative, find the maximums, and use the ... | |
| population model | 7/23/2008 |
| Q: 1/P(dP/dt)= aP + b I know to separate the variables, but I was told to use partial fractions to ... A: Wel, I'm back now and I thought about the problem. Here's how I solved it (what I came up with was ... | |
| Trig Functions | 7/22/2008 |
| Q: Find the 6 trigonometric values of Θ = cos^−1 (3/7). Give exact answer. A: They might mean the second approach I took, or they might mean to find the six trig functions on an ... | |
| Calculus - Related Rates word problem | 7/21/2008 |
| Q: I'm having trouble picturing a word problem and thus having trouble discerning what the appropriate ... A: The width is 3 at the top and 0 at the bottom. The have a height of 1 foot. Using these two pieces ... | |
| Calculus 1 | 7/21/2008 |
| Q: Scotto. I am having trouble with a problem, please help me with this:"Average cost" A manufacturer ... A: C(x)=450+30x+0.08x² (A) To find the average, integrate C(x) from the minimum number to the maximum ... | |
| Integration | 7/21/2008 |
| Q: How do you evaluate this definite Integral : Integral of (x^2)*e^(-x^2) with limits from 0 to 1? I ... A: Let u=x, so du=dx and dv=xe^(-x²), so v=e^(-x²)/2. This problem fits in with the u-v problems where ... | |
| Integration | 7/20/2008 |
| Q: I'm a Math teacher myself, and I'm mystified by what I thought was a simple problem: to integrate ... A: That's the only way I know how to do the problem. If the answer is known it can be seen to be ... | |
| integrals | 7/17/2008 |
| Q: I've had Calculus 2 before, but am taking it over because it's been about 9 years since I last had ... A: Out of an article (//en.wikipedia.org/wiki/Riemann_sum), I have taken the following: "In ... | |
| Inequalities | 7/16/2008 |
| Q: 1) f(x)= (2x-3)/(x-5) What is modulusf(x)modules > (or equal to) 3/2. I have found the answer of ... A: 1) If f(x)=(2x-3)/(x-5), then by what you have said the mod looks like it takes the absolute value ... | |
| Calculus-Related Rates | 7/15/2008 |
| Q: I tried to work on these problems but I'm not completely sure how to start it and if I was doing it ... A: The car is moving one way at 15 m/s and the boat is moving 4 m/s. Multiply the speed by 5 seconds to ... | |
| derivative | 7/15/2008 |
| Q: The fundamental concept of the derivative is convergence to a limit..ie an unknown value can be ... A: If you had a simple function, for example, f(x)=x+2 for all x>0, then f(0) would not be defined. ... | |
| Inequalities | 7/15/2008 |
| Q: 1) f(x)= (2x-3)/(x-5) What is modulusf(x)modules > (or equal to) 3/2. I have found the answer of ... A: Sorry for the error in my answer to 2. It should have read: 2) Note that the answer needs x=a ... | |
| Inequalities | 7/13/2008 |
| Q: 1) f(x)= (2x-3)/(x-5) What is modulusf(x)modules > (or equal to) 3/2. I have found the answer of ... A: For future references, ≥ is alt-242 and ≤ is alt-243. 1) I'm not sure what ... | |
| an angle problem | 7/10/2008 |
| Q: I'm hoping you can help me! Here's theA boat is being pulled by rope towards a dock that is 6 feet ... A: It is known that 6²+y²=x² where y is the diagonal and x is the base of the right triangle with the ... | |
| differentiation | 7/10/2008 |
| Q: sir how can i find the derivative of x raise to the power 5/2 by definition method? actually this ... A: I'm not entirely sure what, 'derivative of x to the power 5/2 by ab initio method.can you solve it ... | |
| rate of change in rectangle | 7/10/2008 |
| Q: I'm having difficulty setting these equations up. Any help would be greatly appreciated! Robert ... A: dL/dt = -2, dW/dt = 2, L=12, W=5 Area is A=WL, perimeter is P=2W+2L, lengths of the diagonal of the ... | |
| Delta-epsilon proof | 7/10/2008 |
| Q: I need to do a delta-epsilon proof for the limit as {x goes to (5pi)/3} for cosx. I kind of ... A: Using the Taylor's polynomial to approximate the cos(x) curve around x=2π/3, we get ... | |
| Pre-cal Trigonometry | 7/9/2008 |
| Q: I'm currently taking pre-cal, but I just don't understand how to simplify, solve and varify using ... A: sin^3(θ)-cos^3(Θ)= (1+sin(θ)cos(θ))(sin(θ)-cos(θ)) In the difference ... | |
| differentiation | 7/9/2008 |
| Q: sir how can i find the derivative of x raise to the power 5/2 by definition method? actually this ... A: To raise a number to the x to the 5/2 power, take the squareroot and raise it to the 5th power. ... | |
| calculus | 7/8/2008 |
| Q: i trying to find dx/dy of 2x^3 - 3x^2y + 2xy^2 - y^3 = 2 i came up with dx/dy = -6x^2 + 6xy - 2y^2/ ... A: That answer is almost right except that it left out y' (dy/dx). The derivatives of each of the ... | |
| MVT | 7/8/2008 |
| Q: I am working on a Mean Value Theorem problem and I was hoping you could take a look at my ... A: Incorrect for solving: The first method gives the average of the two endpoints only. The second ... | |
| composite functions | 7/8/2008 |
| Q: ...I am working on a composite function question and i am sort of lost. The question is: Let K(x) ... A: This looks like one of those problems where they supply so much information so that people get ... | |
| Calculus | 7/8/2008 |
| Q: 1.I am integrating sqrt(x^2+a^2) by parts,but I came to the point when I have find the derivative of ... A: 1. The problem needs to be integrated by a trig substitution. Draw a right triangle with the far ... | |
| Taylor's series | 7/7/2008 |
| Q: With the aid of anything (excel , computer code), how can I argue that the series 1+1/2+1/3+1/4+1/5 ... A: This series can be made into a function f(x)=int(1/a) on [a-1,a] for all a from 1 to ∞. The ... | |
| calculus | 7/3/2008 |
| Q: calculate the area between the curves(transedental): 1.f(x)=2sin(x) g(x)=tan(x) ... A: The curves given are 1.f(x)=2sin(x) g(x)=tan(x) 2.f(x)=2sin(x)+sin(2x) 3.f(x)=x^3-x^2=-x^2+9 I am ... | |
| maths+trigonometry | 7/3/2008 |
| Q: prove that: sin^2(x) + cos^2(x) = 100 ANSWER: Take a triangle with b as the near side, a as the ... A: The 100 is actually in the question that was asked by you. This is what was in ... | |
| maths question | 7/2/2008 |
| Q: please give me the proof of the equation Cos2X+Cos2Y+Cos2Z=1 A: This is just like a three dimensional triangle. The Pythagorean theorem states that a²+b²=c² when ... | |
| calculus | 7/2/2008 |
| Q: 1. If A and B are constants, show that the derivative with respect to x of each of the following ... A: I'll assume in both cases that the exponet is done before the trig funtion. If not, let me know. ... | |
| Numbers | 7/2/2008 |
| Q: What are numbers? A: Numbers are numbers. They could be positive integers: 1, 2, 3, 4, etc. They could be negative ... | |
| simplifying | 7/1/2008 |
| Q: how can this be simplified? sin(5lnx). A: One way would be to say that sin(5ln(x))=sin(ln(x)^5). ... | |
| limits | 6/30/2008 |
| Q: Limit sin-x (sin inverse X) x->0 ------- x A: Is this problem lim(x->0)((sinx-x)/x)? You can a) apply L'Hosital's rule b) put in the Taylor's ... | |
| calculus I (geometry) | 6/29/2008 |
| Q: If you have a moment I could uses a little assist, I was trying to work this problem from my calc ... A: D1²=(x+2)²+(1-0)²=x²+4x+5, D2²=(x-3)²+(4-0)²=x²-6x+25, and D3²=(3+2)²+(4-1)²=34. D1 hypoteneuse Is ... | |
| differential | 6/29/2008 |
| Q: could you give me the reason for choosing f'(x)=0;if f(X)is a real function?and also could you give ... A: The reason for choosing f'(x)=0 if for finding the extreme points of the function since when an ... | |
| Preliminaries, Polar Coors, Complex numbers | 6/28/2008 |
| Q: Good day Scotto, thanks for helpin out on these 2 qns that have been bugging me lately... 1)How do ... A: 1) Note that both of the curves start at (0,1) since sin(0) is 0. Doing this problem we will take ... | |
| finding the equation of the tangent line | 6/27/2008 |
| Q: My problem is: The point P(5,2) lies on the curve y=sqrt(x-1). Find an equation of the tangent ... A: I'm not sure if that's the right direction or not. Here is what I do know. To find a tangent line, ... | |
| Calculus I (Substitution Rule and Definite Integrals) | 6/26/2008 |
| Q: Please help! I'm not sure how to do this one and I must have it done by tomorrow (6-27-08)! I was ... A: Have you ever done ∫u dv = uv - ∫v du? Let u=x, then du=dx. Let dv = 1/(sqrt(1+2x)) dx, ... | |
| calculus | 6/24/2008 |
| Q: A conical tank (with vertex down) is 20 ft across the top and 24 ft deep. Water is flowing in to the ... A: The volume of a conical tank is pi*r^2*h/3 where r is the radius and h is the height. We know that ... | |
| radian interval notation | 6/24/2008 |
| Q: f(x)= 1/sqrt(1+sin x) Tell where f is continuous. Give your answer in interval notation. I know it ... A: I'd not try to write it with parenthesis. I'd put all 'The function f is continuous at all real ... | |
| calculus | 6/22/2008 |
| Q: I have finished most of my calculus homework assignment, but I can't seem to figure out these ... A: The derivative of ln(f(x)) is f'(x)/f(x). The derivative of e^f(x) is f'(x)e^f(x). The derivative ... | |
| Exponentials | 6/22/2008 |
| Q: Mathematical proof of f(0) = 1 where f(x)= a^x. A: x^n means take 1 and multiply it by x for a total of n times. Since x, the number times it is ... | |
| differential calculus applications | 6/22/2008 |
| Q: what is meant by critical point,stationary point,absolute maximum,local maximum,absolute ... A: A critical point is any of the following: I don't know what is meant by a, 'staitionary point'. ... | |
| Calculus I (Indeterminate Forms and L'Hospital's Rule) | 6/20/2008 |
| Q: I hope you can help! I am taking a college first year calculus correspondence class. I have am ... A: Q1: Yes, you are correct - It's (1/(xln(x)))/1. Let x approach infinity on the top and bottom and ... | |
| College Calculus II | 6/20/2008 |
| Q: OK I need help. I took this class spring semester at UT austin and failed. So now I am taking it at ... A: As long as there weren't too many questions on the exam, you could type in all of the problems and ... | |
| Calculus - Separation of Variables | 6/19/2008 |
| Q: I am doing a problem for Calc. 2 and I can't seem to finish it. The problem is: Use separation of ... A: Separate the problem into ye^(-3y)dy = sin^2(t)/sec(t)dt. On the left side do integration by parts ... | |
| calculus | 6/19/2008 |
| Q: I am doing a set of problems on implicit differentiation and have run across the following problem ... A: Lets let y^2 = dx so that we don't get confused. 2y(dy/dx)=d, so dy/dx=d/(2y). At the point ... | |
| Arc Length of Sine Curve | 6/16/2008 |
| Q: A particle moves at a constant speed of v m/s along a sinusoidal path. The path is described as y = ... A: To find the arc length of a curve, the equation must be solved from 0 to a using the integral (0 to ... | |
| vectors.. | 6/15/2008 |
| Q: i don't know how to draw the diagram, I'm having a great deal of trouble interpreting the question. ... A: I'll assume that the crank is being pushed at the opposite end of where it is anchored. I'll also ... | |
| curve sketching | 6/13/2008 |
| Q: how do i determine the x and y intercepts of the function to being the rest of this curve sketching ... A: The way that most people have learned to write the function (for future use) is y = 3x^2-1/x^3. The ... | |
| Calculus Early Vectors Section 4.4 | 6/13/2008 |
| Q: the question is F(X)= cos(ln x) A: The derivative is the chain rule. You have f(g(x)), so the derivative is f'(g(x))g'(x) where ... | |
| calc | 6/12/2008 |
| Q: my question is, using l'hopitals rule what is the limit of (1+3x)^cscx as x approaches zero from the ... A: This problem needs to be rewritten before applying L'Hospital's rule. Any function f(x) can be ... | |
| Solving acceleration problems | 6/9/2008 |
| Q: I dont know if this is your field but if you could help me at all Id really appreciate it. A object ... A: Maybe I should put in there I know some physics and some chemistry as well (since I do). The basic ... | |
| Calculus | 6/8/2008 |
| Q: Determine a pattern for the nth derivative of f(x)=1/(6x+6), prove your pattern by finding the 4th ... A: Note that x is always in the denominator for all of the derivatives, so we have a negative power on ... | |
| Optimization.. | 6/8/2008 |
| Q: I have no clue where to start....Here is the question.. An apple orchard now has 80 trees planted ... A: If we have 80 trees, the production is 400 apples / tree. Looking at the units, these would need to ... | |
| triangle optimization problem | 6/5/2008 |
| Q: consider a square piece of paper with sides equals to 1 unit. we label the four vertices as ABCD. ... A: Flip the square over so BC is on the right side and call A the origin. It is known that for any ... | |
| Vectors | 6/5/2008 |
| Q: I have looked at this question for so long but can't figure out where to start. Any help you can ... A: I believe that the sum of two vectors is in the same plane as the two vectors. Since they are both ... | |
| Optimization | 6/4/2008 |
| Q: A man walks down a hallway carrying a long piece of wood. This particular hallway is a bit narrow, ... A: Elaborate more on where you got it from. According to the way I found to do it (which turns out to ... | |
| Optimization | 6/4/2008 |
| Q: A man walks down a hallway carrying a long piece of wood. This particular hallway is a bit narrow, ... A: To differentiate 6/sin(t) + 4/cos(t), the answer is -(6/sin^2(t))(cos(t) - - (4/cos^2(t))sin(t), ... | |
| Integration by trig Substitution | 6/4/2008 |
| Q: I integrated this problem by trig sustitution. Could you please review my answer exspecially when I ... A: The real answer is ln(x/2 + sqrt(x^2-4)/2) )+ C = ln(x + sqrt(x^2-4)) - ln(2) + C = ln (x + ... | |
| Optimization | 6/3/2008 |
| Q: A man walks down a hallway carrying a long piece of wood. This particular hallway is a bit narrow, ... A: It says that the wood needs to carried horizontally, but it can be carried at an angle so that some ... | |
| Calculus | 6/3/2008 |
| Q: There is a room in the shape of a cube with a side length of 4 meters. Imagine a scorpion, located ... A: That seems like the best way is to unfold the room. All you've got to do is draw it out on graph ... | |
| Calculus | 6/2/2008 |
| Q: There is a room in the shape of a cube with a side length of 4 meters. Imagine a scorpion, located ... A: Since the room is a cube, there are three different ways the scorpion could move. Since it is a ... | |
| continous | 5/31/2008 |
| Q: I am megahana and undergraduate student. I am not understanding that, 1) what is exact difference ... A: 1. Continuous means a curve can be drawn fron left to right to represent the function without ... | |
| integral | 5/29/2008 |
| Q: I'm in trouble integrating : S dx/(e^(x/2)+e^x). I tried to integrate it as sum but it wasn't ... A: Let t=1+e^(x/2), so 2 dt = e^x dx. After this has been done, split the integral using A/u + B/(u-1) ... | |
| calculus diferrentiation | 5/29/2008 |
| Q: evaluate lim (|x - 4|) / x-4 x-4 ANSWER: I almost didn't answer this - that's because there is ... A: The absolute value is the positve value: Examples: |1|=1, |-4.6|=4.6, |5.02|=5.02, |-565/3|=565/3. ... | |
| calculus diferrentiation | 5/28/2008 |
| Q: evaluate lim (|x - 4|) / x-4 x-4 A: I almost didn't answer this - that's because there is no answer! (tee hee hee...) But seriously, ... | |
| ap calculus | 5/27/2008 |
| Q: Let v(t) be the velocity, in feet per second, of a skydiver at time t seconds, t>0. After her chute ... A: Note that when falling under gravity, the equation for velocity is v = -9.8t since 9.8 is the ... | |
| ap calculus | 5/27/2008 |
| Q: For what values of a and b does the function f(x)=x^(3)+ax^(2)+bx+2 have a local maximum when x=-3 ... A: To find the maximum and minimum values, the dervative has the value 0. Since the maximum and ... | |
| integration question | 5/18/2008 |
| Q: ) i wanna u tell me the integration of : ln of X to tje powre of 2 over X multiply by radical of 1 ... A: The question, restated, is the integeral(ln^2(x)/(x*(1+ln^2(x))). This is a problem that requires ... | |
| Calculus applying derevitives | 5/17/2008 |
| Q: Here is my problem: Hauling in a Dinghy: A dinghy is pulled toward a dock by a rope from the bow ... A: A. Note there is a triangle h=height=6' and c=diagonal=rope out=10'. If b=base, it is known that ... | |
| Calculus applying derevitives g6 | 5/17/2008 |
| Q: Here is my problem: Melting Ice: A spherical iron ball is coated with a layer of ice of uniform ... A: Convert 8ml to volume. The volume of a sphere is 4pi*r^3/3, where r is the radius, which is half of ... | |
| Optimizing Functions | 5/12/2008 |
| Q: I just wanted to know some easy steps to optimizing functions. I have a Calculus final in two days, ... A: To optimize a problem, set the derivative, f'(x), equal to 0 and solve for x, giving x0. If the ... | |
| Calculus Question | 5/12/2008 |
| Q: Find an equation of the line passing through (2,5) and perpendicular to y=3 x+1. A: That's y=3x+1, right? Note that they were on spli t lines, just like this... The equation is ... | |
| related rates | 5/9/2008 |
| Q: The base of a pyramid-shaped tank is a square with sides of 8 meters long and the vertex of the ... A: Let x be how high we are from the ground. The width at the ground is 8 and the width at height 11 ... | |
| approximation to the definite integral | 5/9/2008 |
| Q: Obtain an approximation to the definite integral I = 2/√п ∫e^-x^2 dx (integral ... A: The Taylor's series for e^t is sum(0 to infinity)(t^n/n!) In this problem, t is to be -x^2. Given ... | |
| calculus | 5/7/2008 |
| Q: I want to make a fish tank with a volume of 2 m^3 and I would like the base of the tank to be a ... A: l=length, w=width, h=height, and Volume=v=2=lwh. The equation for volume v can be solved for height ... | |
| calculus | 5/6/2008 |
| Q: I want to make a fish tank with a volume of 2 m^3 and I would like the base of the tank to be a ... A: I have found that the measurements to minimize the cost are base=13.73657091", length=27.47314182", ... | |
| precalculus | 5/6/2008 |
| Q: I'm taking my first class in a LONG time and I'm having problems verifying this identity: sin(2 ... A: What this looks like is sin(2t) = 2 tan(t)/1+tan^2(t). Note that sin(2t) = 2sin(t)cos(t) and that ... | |
| Limits | 5/4/2008 |
| Q: lim approaches 0 equation= sin4x/5x A: It is known that sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x). Using these, ... | |
| functions | 5/4/2008 |
| Q: The function f(a)=max(a,1/a) for all a>0. Find the values of f(r)*f(1/r) for 0<r<1." A: Since r is between zero and one, one over r is greater than one. This means that one over r is the ... | |
| Rational Functions | 5/3/2008 |
| Q: I'm having trouble to solve and graph this rational function: f(x)= x^3-x^2-6x/x^2-3x+2 Can you ... A: Use x-3 on top and determine the other factor. On the bottom, use x-1 and determine the other ... | |
| calculus | 5/2/2008 |
| Q: find the exact dimensions of the largest rectangle that can be insribed in the curve y= e^x ... A: The second quadrant is where y is positive and x is negative (but you probably already knew that). ... | |
| "e" and log | 5/1/2008 |
| Q: well I've been having a lot of trouble with this, cause I can't find a way to demonstrate this is ... A: I am use to writing logarithms in two different ways. Log usually refers to using base ten, whereas ... | |
| calculus exam | 4/30/2008 |
| Q: how to intergrate 1) sin(14x) cos(5x) dx 2) 2.7^2x+7 dx A: 1) Use three trig identities and simplify the first one. The identies are sin^2(x) + cos^2(x) = 1, ... | |
| Calc | 4/30/2008 |
| Q: I am having trouble evaluating F(x)=(intagral from 0 to x) of sin^2tdt. Then find F' and relate the ... A: There is a trig formula that relates sin^2(t) to an angle of half size. If y is suppose to be F, ... | |
| Related rates? | 4/28/2008 |
| Q: At noon ship A was 100 miles due east of ship B. Ship A is sailing west at 12 miles per hour and ... A: Put ship B at the origin. Ship A has the equation -100+12t=x with y=0. Ship B has the equation ... | |
| Calculus-Acceleration, velocity and position | 4/28/2008 |
| Q: A projectile is fired straight up from a platformn 10 feet above the ground, with intial velocity of ... A: The initial velocity is 160ft/s. This would lead to a 160t where t is measured in seconds. Gravity ... | |
| Calculus Problems | 4/28/2008 |
| Q: I have a question that i cant seem to figure out... Let f(x)=ax+ b/x where a and b are constants. a) ... A: Note that the funciton f(x) can be looked at as a*x^1 + b*x^-1. The derivative of x^n is n*x^(n-1). ... | |
| Work | 4/27/2008 |
| Q: It is reported that the Great Pyramid of Egypt was built in 20 years. If the stone making up the ... A: By the 'total amount of work done', I assume they are referring to lifting the stones into place. ... | |
| vector calculus | 4/27/2008 |
| Q: Consider the surface z = f(x,y). Confirm that m = (-fx,-fy,1) is normal to the surface and that u ... A: Two vectors are said to be perpendicular if the dot product is zero. Two points are parallel if u = ... | |
| second derivative | 4/25/2008 |
| Q: i already found f'(x) but now i need to find f"(x). So I need the derivative of -1/x^2(x^2+1)^1/2. ... A: If the function given is 1/(x^2(x^2+1)^0.5), look at it as 1/(f(x)g(x)) where f(x)=x^2 and ... | |
| Pet Project | 4/24/2008 |
| Q: I work in a restaurant that sells items similar to those in a competing restaurant, and was ... A: I think I would choose the ingredients you want to look at and make a list of them. Also make a ... | |
| calculus-shadow problem | 4/24/2008 |
| Q: ray needay is 6 ft tall and he is walking away from a 24 ft tall lamp post at 4 ft per second. how ... A: This looks like two similar triangles. Let y be the shadow length and x be the distance from his ... | |
| Trig Substitution | 4/24/2008 |
| Q: I have performed a trig substitution on this integral. My Book answer is: -Arctan[1/sqrt(x^2-1)] ... A: I tried doing this problem and I got the same thing. The answer is 1, the integral is theta, and ... | |
| calc | 4/21/2008 |
| Q: a swimming pool whose bottom has area 5000/3.14 square feet is to be built in the form of a ... A: Let the circle have radius r. The area of both of the ends (the two semicircles) is pi*r^2. The ... | |
| Another Optimization Problem... | 4/21/2008 |
| Q: A rectangle PQRS is inscribed in the region between the x-axis and the part of the graph y= cos 4x ... A: What I did was an error - I was starting to think that the area was somehow involved. After reading ... | |
| calc | 4/20/2008 |
| Q: a swimming pool whose bottom has area 5000/3.14 square feet is to be built in the form of a ... A: What you would have for area would be a circle (the two ends when joined) and a rectangle. Find the ... | |
| Another Optimization Problem... | 4/20/2008 |
| Q: A rectangle PQRS is inscribed in the region between the x-axis and the part of the graph y= cos 4x ... A: The cos(x) curve has a maximum of 1 at x=0, which means length of the base is x - -x = 2x. The ... | |
| Optimization Problem | 4/20/2008 |
| Q: A piece of wire 8cm long is cut into two pieces. One piece is bent into a circle, and the other is ... A: Let x be the length of wire that is cut for the circle. The length left for the square is 8-x. For ... | |
| integral | 4/18/2008 |
| Q: integral of 9sin(square root t+1) A: The only way I see it can be done is to use the Taylor's series for sin(x). It is sum(n=0 to ... | |
| Optimization problem... | 4/18/2008 |
| Q: In this question it says: A fence 8ft tall runs parallel to a tall building at a distance of 4 ft ... A: The fence is 8ft tall and 4 from the building. Construct a triangle with some base y between the ... | |
| calculus | 4/17/2008 |
| Q: is the following series convergent or divergent? summation of sin2n/1+2^n from n=1 to infinity. A: If sin2n/1+2^n is really suppose to be sin2n/(1+2^n) since the addition wants to be done first, it ... | |
| calculus | 4/17/2008 |
| Q: Is the following series absolutely convergent, conditionally convergent, or divergent? 2/5 + 2/5*6/8 ... A: Notice how the multipliers care increasing. The top goes 2 6 10 14 ... and the bottom goes 5 8 11 ... | |
| derivatives | 4/17/2008 |
| Q: I am stumped on these 2 questions. Please help!! 1) The revenue generated by the sale of x bicycles ... A: Marginal revenue is found by taking the derivative. The derivative of ax^n is nax^(n-1). Example: ... | |
| Inequalities | 4/16/2008 |
| Q: I need help to find all the inequalities and identify the variables. Thank You. An automobile ... A: Let c1 be the cars at Detroit and t1 be the trucks at that place. Let c2 be the cars at Cleveland ... | |
| Two tough calculus max and min problems??? | 4/16/2008 |
| Q: I have been having trouble with this section. especially this two word problems with max and min. ... A: 1. It can be written as ar^2 + b/r^5. Take a derivative in terms of r and set it equal to 0 to find ... | |
| math | 4/15/2008 |
| Q: The average of x, 1, 2, 3 is 4, find the average of x, 1 and 2. ANSWER: The average is the sum of ... A: Hour Hand Note that there are 30 degrees in an hour. The hour hand is at 30h depending on the hour ... | |
| help in trignometry | 4/15/2008 |
| Q: radian-degree converstion @rad=πrad/180(75)=5π/12=1.31 OK the question is how did the ... A: I'm sorry that I responded with the wrong answer. Thank you for explaining more clearly the answer ... | |
| math - calculus | 4/14/2008 |
| Q: I wish to use 300 meters of fencing to enclose a rectangular plot. Part of the fencing will be used ... A: Problem: Maximize area A=WL; use 3W+2L=300. I get that you should divide the fence in half. Divide ... | |
| Parametric equations | 4/14/2008 |
| Q: I have come to a bit of a standstill with the following problem, in fact I have spent the past 4 ... A: This is a right triangle. The square of the distance can be found as x^2 + y^2, putting in what x ... | |
| Cal help | 4/14/2008 |
| Q: Let f be the function defined by f(x)=ln(2+sinx) for pi less than or equals to x less than or equals ... A: 1. It is known that ln is an increasing function, so find the maximum value of sin(x) on (pi,2pi). ... | |
| AP Calculus | 4/14/2008 |
| Q: My teacher assigned this question in our homework over the weekend and I want to know if I'm on the ... A: The length of the hypoteneuse is y and the two legs are then y/root(2). The area of each of these ... | |
| Calculus | 4/13/2008 |
| Q: If you can help me answer this problem that wouls be greatly appreciated. A company wishes to ... A: Take h=height, w=width, and l=length, then we have v=volume=52=hwl. We know that l=2w, so volume we ... | |
| The most northwest point | 4/13/2008 |
| Q: If an irregular shape is represented by the coord. set [(x1,y1), (x2,y2)...(xn,yn)], how can its ... A: I don't see where an integral would do any good. There is no way to find it mathemtically if the ... | |
| Min and Max on an Interval | 4/12/2008 |
| Q: I'm stuck on a calculus problem. I think I'm solving it right but my answer doesn't really seem to ... A: Before taking the derivative, I would simplify the function a little bit. You have stated how to do ... | |
| calculus | 4/12/2008 |
| Q: Let R be the region between the x-axis and the graph y=2x-x^2 about the x-axis. Now i am having a ... A: Sove and see where 2x-x^2 is equal to 0 by saying that the function factors to x(2-x). This will ... | |
| Related Rates | 4/11/2008 |
| Q: The cross-section of a water trough is an equilateral triangle with a horizontal top edge. If the ... A: A meter is 100 cm for the length. The trough is an equilateral triangle, so when it is cut in half ... | |
| exponential derivatives | 4/11/2008 |
| Q: I'm really stuck with a calculus question, I was wondering if you could help me out: What is dy/dx ... A: Taking the ln of both sides gives xy = ln(x). This is where the hint takes you, but there is one ... | |
| probability density function | 4/11/2008 |
| Q: A machine component has a useful life of 0 to 10 years and the probability density function modeling ... A: The function really should be 0.42377x/(x^2+0.9) - right? Try u substitution with u = x^2 + 0.9, du ... | |
| sorry to ask ANOTHER | 4/8/2008 |
| Q: to compute the 99th derivative of a trigonometric function, would i just continue to take the ... A: You've noticed the pattern - the 4th, 8th, 12th, 16th, 20th, ... 88th, 92nd, 96th derivatives hae a ... | |
| Calculus?? | 4/8/2008 |
| Q: 5. (a) Find the equation of the tangent line to y = 1 x at the generic point (a, 1/a) (b) Let f ... A: This was all I got: '(b) Let f (a) be the area of the triangle bounded by this tangent line, the x- ... | |
| Calculus?? | 4/8/2008 |
| Q: 5. (a) Find the equation of the tangent line to y = 1 x at the generic point (a, 1/a) (b) Let f ... A: It looked like you started to ask another question, but I accidentally sent you the same answer. ... | |
| Calculus | 4/5/2008 |
| Q: A man 2m strolls at 1m/s along the edge of a road 10m wide. A street light 6m high stands on the ... A: The ratio of 6:2 is the ratio of the heights, so the distance to the lamp on the ground is 3 times ... | |
| minimizing multilpe variable | 4/4/2008 |
| Q: An aquarium is being built in the shape of a rectangular solid. The top is open, the sides are ... A: Give the tank height h, width w, and length l. When they are all multiplied together, tht total ... | |
| CALCULUS | 4/4/2008 |
| Q: EVALUATE THE FOLLOWING INTEGRAL 1 $e^-x draw rough sketch of the following 1 1 - e^-x A: The derivative of e^f(x) is e^f(x)*f'(x). In the first one, f(x) is only -x and we can see that ... | |
| Calculus | 4/4/2008 |
| Q: A window is to be made in the shape of a square surmounted by an equilateral triangle. Describe the ... A: The square is have the same edge as the triangle, which is probably an equilateral triangle. Add ... | |
| Calculus | 4/3/2008 |
| Q: If f(x)=e^-(1/x+1) I reall y am not getting how to do problems involving e, I know to take the ... A: If f(x)=e^-(1/x+1) I really am not getting how to do problems involving e, I know to take the ... | |
| second-order partial derivatives | 4/2/2008 |
| Q: How are all the second-order partial derivatives of the function z = 9xln(8x^3y)worked out? Thank ... A: The second order partial with respect to x is found by treating y as a constant and with respect to ... | |
| sum of all as N goes from 1 to infinity of the function (1/2^n^2) | 4/1/2008 |
| Q: I know what the answer is for (1/2^n). It's simply 1. But what does it become when you square n? ... A: The answer for 1/k is k/(k+1) if the first term is n=0. For n=1 and k=2, the sum is 1. For the ... | |
| Volume and Surface Area question. | 3/31/2008 |
| Q: The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per ... A: For a cone that has a height larger radius R and a smaller radiud r. The formula is pi(R^2 + Rr + ... | |
| An inverted pyramid drainage problem | 3/31/2008 |
| Q: Could you please help me with this question. I do not understand how to answer it. I am currently ... A: a. Take the equation for volume and note that if B is x^2, then h is 5x/4. Put both of these ... | |
| area | 3/31/2008 |
| Q: A rectangle has one side on the x-axis and the upper two vertices on the graph of y = e^(-2x^2) give ... A: The maximum possible area would be found if y were as big as possible. The functions to find the ... | |
| Taylor Series sin(3x) | 3/30/2008 |
| Q: I have to write a taylor series for f(x)=sin(3x) where c=pi/3 What is the series, interval, and ... A: The Taylor's Series is f(n)(x0)*f(x0)/n!. f(n)(x0) is the nth derivative of f(x) evaluated at x0). ... | |
| continuity | 3/28/2008 |
| Q: my question is "for what values of x is the function f(x)= e^sinx / (4 - (x^2 - 9)^1/2)? i'm very ... A: Do you mean for what values of x is f(x) defined or what is it's range? First, lets take care of ... | |
| differentiate composite funtion using chain rule | 3/28/2008 |
| Q: . my name is fiza. i really don't havea any idea how to solve : 4ln(ln(ln(secx)))and tan^3 ... A: Remember what the chain rule says: To find the derivative of f(g(x)), it's f'(g(x))*g'(x). What we ... | |
| calculus 1 | 3/28/2008 |
| Q: PLEASE REPLY BY TONIGHT!! REALLY APPRECIATE IT!! and also if u can explain the answers in steps..=D ... A: I didn't turn it on until this morning, but here goes. 1) Since coth(x) = sinh(x)/cosh(x), the ... | |
| Really need your help.. asap! | 3/27/2008 |
| Q: The question is.. Use the sum and difference formulas and the sin2x and cos2x to express sinx^0 ... A: This is what I read, written in proper mathematical notation: Use the sum and difference formulas ... | |
| integral and avg mean value | 3/25/2008 |
| Q: Let f be a continuous function that is defined for all real numbers x and that has the following ... A: a) Since this was asked first, all you can do is approximate the average between 1 and 3 by taking ... | |
| Related Rates | 3/24/2008 |
| Q: A water trough is 6m long, and its cross section has the shape of an isosceles trapezoid that is ... A: I must not have been paying close enough attention to the problem as I usually do. The 20 is the ... | |
| Related Rates | 3/24/2008 |
| Q: The trunk of a tree is approximately cylindrical in shape and has a diameter of 1m when the height ... A: I'm not sure where the answers came from, though they might be right. The volume of the trunk is ... | |
| simplex algorithm | 3/24/2008 |
| Q: I need to find the inequalities that must be satisfied. A furniture-finishin plant finishes two ... A: The profit equation is given by 5A + 3b. The two constraints are 8A + 12B <=480 and 9A + 6B <= 360. ... | |
| Double Integrals | 3/21/2008 |
| Q: I am having difficulty starting the following problem. Find the value of the double integral I= ... A: Integrate with respect to x and with respect to y separately. When this is done with respect to x, ... | |
| calc | 3/20/2008 |
| Q: Suppose that a square sheet of aluminum is placed in the hot sun. It begins to expand very slowly so ... A: The sides are the side of a right triangle and both equal, so 2s^2=d^2 where s is the side length ... | |
| calculus | 3/20/2008 |
| Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley ... A: This is a calculus / trig problem. We have a triangle where the base is 8 meters that is decreasing ... | |
| Vector calculus | 3/19/2008 |
| Q: A certain objects velocity vector has components vx(t)=bt^2+c, vy(t)=qt, and vz(t)=0, where b=10 ... A: Acceleration is the derivative of velocity. Magnitude is the squareroot of the sum of the squares ... | |
| help | 3/18/2008 |
| Q: when determining higher order derivatives, do you always expect to eventually get "(d^n)y/dx^n=0 A: Usually (d^n)y/dx^n means the nth derivative. (d^1)y/dx^1, usually written as dy/dx is the first ... | |
| polynomials | 3/14/2008 |
| Q: how can i find the graph & the equation for these two statements: - An odd-degree function with 3 ... A: Odd degree means all of the exponets are odd. If there is one max/min, the order on x is 1+1. If ... | |
| AP calculus | 3/13/2008 |
| Q: I have had previous experience in Calculus but have not done any maths for a few years now and ... A: Remember that the derivative of x^n is nx^(n-1) and proceed from there. In the domain, find the ... | |
| Calculus | 3/13/2008 |
| Q: Equation: y=.27X^3-6.31X^2+29.87X+34.7 with the relationship between x given as gross domestic ... A: The derivative of x^3=3x^2, x^2=2x, etc. This is what I understand to be the derivative, and what I ... | |
| Calculus | 3/13/2008 |
| Q: COuld you please help me with the following calculus problem: Given g(x) = x^(1/3) (x²-4), find all ... A: Yes, it is correct. The only place to go from here might be to put them in a fraction with x^(2/3) ... | |
| parametric | 3/12/2008 |
| Q: as t varies, the following parametric equations trace out a line in the plane x= 2+ 3T y= 4+ 7T ... A: a) If T is nonnegative, set T = 0 and find the minimum value for x and y. b) A better way of asking ... | |
| second derivatives | 3/6/2008 |
| Q: After having found f '(x)= 2(1-x^2) / sqrt 2-x^2 ( from the given function: f(x)= x(sqrt 2-x^2) I ... A: This is a quotient rule with f(x)=2(1-x^2) and g(x)=(2-x^2)^0.5. The quotient rule I remember as ... | |
| calculus bc | 3/5/2008 |
| Q: function is definded by f(x) = 1/3 + 2/3^2 + 3/3^3 + ....+ {[(n+1)/3^(n+1)]*x^n} a, Find the ... A: Is the x^n suppose to be in every term in the series? I assume so, though it's not in the first ... | |
| Trigonometry Formulas | 3/4/2008 |
| Q: Okay, this is something that has been bugging me for several months. I would like to know what the ... A: Take A as the angle of the hypoteneuse with far side a, near side b, and hypoteneuse c. Note that C ... | |
| i dont understand | 3/4/2008 |
| Q: I don't know how to solve this problem: Find the area between the lines y=x, y=3x, and x+y=4 using ... A: Solve for the x values at the points of intersection of the 3 lines. Order these points from ... | |
| calc | 3/3/2008 |
| Q: A woman is walking directly toward the State House in Montpelier at a constant rate of 1.5 meters ... A: First, note that the 1.5 is in meters / second and the other two numbers are in feet. After ... | |
| help | 3/3/2008 |
| Q: A certain calculus student hit Mr. Leacher in the head with a snowball. If the snowball is melting ... A: That's a pretty big snowball if the radius is 1 foot! And another has raidus 2 feet? The volumne v ... | |
| calc question | 2/29/2008 |
| Q: Slag left over from the manufacture of cement is being piled outside a cement plant. The resulting ... A: The equation for the volume of a cone is (pi)r^2h/3 where r = radius of the base, h=height in the ... | |
| math question | 2/28/2008 |
| Q: How would you solve the following problem? Can it be done in the calculator? Let R be the shaded ... A: If you have a calculator that can do integrals, it can be done. Otherwise, find the intersection ... | |
| Gr.12 Calculus - related rates | 2/28/2008 |
| Q: A sports car and a transport leave a gas station at the same time. The sports car travels east at ... A: It all comes down to applying the formula to find the length of the hypoteneuse c given sides a and ... | |
| AP Calculus | 2/28/2008 |
| Q: Let f be the function given by f(x) = 2ln(x^2 + 3)- x with domain -3 < x < 5 = = ... A: Take the first derivative, set equal to 0. This will tell you points that are max / min for the ... | |
| Calculus | 2/27/2008 |
| Q: Let f be the function defined by f(x)= 2xe^-x for all real numbers of x. A.) Write an equation of ... A: A) The horizontal assymptote can be found by noting that f(x) is always positive. For large x, the ... | |
| Calculus | 2/27/2008 |
| Q: A particle moves on the x-axis so that its velocity at any time t is greater than or equal to zero ... A: To find a maximum, differentiate the function and set it equal to 0. There is no need to do this, ... | |
| Calculus | 2/25/2008 |
| Q: How do you find the equation of the tangent to f(x)= (2x-1)³ where x=1 A: If that f(x)=(fx-1)^2? I can't tell exactly what the exponent is, but on the derivative is ... | |
| How to find the vertex of a parabola | 2/25/2008 |
| Q: I understand what a vertex is and how to find it on a graph or a graphing calculator but, do not ... A: The first term is 2.75(-2.85)^2 = 15.125, the second term is 11*-2.75=-30.25 and the third term is ... | |
| tangent lines... | 2/25/2008 |
| Q: My question is to find all points on the curve (x^2)(y^2) + x*y = 2 , where the slope of the tangent ... A: The derivative should be found by the product rule with y as a function of x - d(xy(x))/dx = y + ... | |
| Short-Cuts to Differentiation | 2/24/2008 |
| Q: I am looking for feedback for the most part- I worked hard on the problem, but I have doubts and ... A: B) Find the equation for the rate of change. To find the average, integrate this equaition from ... | |
| related rates | 2/24/2008 |
| Q: Sand falls from a conveyor belt onto the top of a conical pile at a constant rate of 9 m^3/min. The ... A: The rate of fall is given, but that gives no indication of how fast the volume is increasing. You ... | |
| Finding the limit | 2/15/2008 |
| Q: How do you find the limit as x approaches infinity of ¡î((12x©ø-5x+2)/(1+4x©÷+3x©ø))? A: What is this? ¡î((12x©ø-5x+2)/(1+4x©÷+3x©ø))? It mistranslates onto my PC. I can't tell what the ... | |
| Calculus | 2/13/2008 |
| Q: I am having a lot of difficulty with this question. Thanks for your help! Q: A boat is pulled by a ... A: A triangle needs to be constructed. The h=height is 12 and the b=base is 13^2-12^2 (13 feet rope = ... | |
| Multivariable Calculus | 2/11/2008 |
| Q: Find the standard equation of the sphere with center (-3,2,4) that is tangent to the plane given by ... A: This is from an article, copyright © 2002-2007 by Karl Dahlke . Given any vector, turn its ... | |
| A Calculus Question under differentiation | 2/10/2008 |
| Q: "Please, i'm having problems with a particular question under calculus. Here it is y=e^2x^2^2x^2 x ... A: The problem starts with a product rule. d(a(x)b(x)) = a'b + b'a. b'a is a/x. a'b, however, is a ... | |
| Hooke's Law Problem | 2/6/2008 |
| Q: If 6J of work is needed to stretch a spring from 10cm to 12cm and another 10J is needed to stretch ... A: Try the integral from 10-x to 12-x of kx = 6 and the integral from 12-x to 14-x of kx = 10, ... | |
| horizontal asymptotes... | 2/6/2008 |
| Q: My question says to find the horizontal asymptotes of: f(x)= sqrt(x^2 + x + 1) - sqrt(x^2-x) I ... A: If you want a common denominator, since the square roots are usually in the numerator, the problem ... | |
| Definite Integral using Substitution | 2/5/2008 |
| Q: I am taking a class over Integral Calculus. Can you please help me with the following problem? ... A: You are right up to where you have I= [1,9] (u+2)/u^(1/2) du Before doing integration, lets split ... | |
| Integrals | 2/4/2008 |
| Q: A rectangular swimming pool is 30 ft wide and 50 ft long. The table below shows the depth h(x) of ... A: Draw the figures on a graph. Between each two points, a trapezoid can be drawn. Some shortcuts can ... | |
| Maths | 2/3/2008 |
| Q: these are a few questions (Permutations) I have attempted.Could you please guide me if I am going ... A: 1. i) If repetions are not allowed, you have n items in any order, which is n! except for the fact ... | |
| Intervals of Continuity... | 1/31/2008 |
| Q: I have trouble with trig functions and I cant figure this out. f(x)= (cos(x))/(sqrt(x-10)). I cant ... A: There are two factors to check for continuity. One of them is division by zero and the other is ... | |
| calculus | 1/31/2008 |
| Q: how do i find Amax of f on [-1,2] A: I assume the question is, 'How do I find a max of f(x) for x on [-1,2].' The way to find a max is ... | |
| Hooke's Law | 1/29/2008 |
| Q: To design the interior surface of a huge stainless steel tank, you revolve the curve y=x squared, ... A: x squared will be written as x^2. Since the height y is a parabola y=x^2, the area at any height y ... | |
| Calc | 1/29/2008 |
| Q: Among all pairs of positive numbers whose product equals 25, find the pair with the smallest sum. ... A: Take x to be one number - then 25/x is the other number. The answer is finding a minimum to x+25/x. ... | |
| Calculus | 1/28/2008 |
| Q: ive asked this before but no luck here goes, Suppose that 2J of work is needed to stretch a ... A: The standard equation for a spring is F=-kx where x is the distance that the spring has been ... | |
| Permutations | 1/27/2008 |
| Q: Also where I have used incorrect notation could you please show me where I have gone wrong. Qu1 A ... A: You look like this can help you. On the first question, given that a box contains 8 cards with n A ... | |
| Math | 1/24/2008 |
| Q: A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on the ... A: Compute the average speed for each period and compute how far is traveled in 2 seconds at that ... | |
| pre calc word problem | 1/21/2008 |
| Q: An open rectangular box with a square base is to have a volume of 15ft^3. find a function that ... A: The box has a height h, a depth d, and a width w. The surface area is the area of the four sides ... | |
| Calculus Questions! | 1/21/2008 |
| Q: We are doing integrals and I can not figure out these three...Can you help me? 1- the integral of ... A: 1. Let u=x^7, du=7x^6 dx. Do another u substituion on the result, and it will be solved. 2. Take ... | |
| applying integrals | 1/19/2008 |
| Q: ok so i have two questions about applying integrals. 1) a rectangle of length l and width w is ... A: 1) I wouled extend the outsides of the triangle all the way to the axis. The problem is then find ... | |
| pre cal trig | 1/14/2008 |
| Q: tan 3pi/8=67.5 tan2xsec2x-tanx=tan4x A: Are the equations 1) tan(3pi/8)=67.5, and 2) tan(2x)sec(2x)-tanx=tan(4x)? Is so, what I use are ... | |
| pre-cal | 1/13/2008 |
| Q: i really need help with these problems below. i have tried finding the answer, but i keep gettin ... A: #1) Take the log base 4 of both side. Then on the right side you can take (log base 4)(4^(6x+2)) ... | |
| 3-d orgin | 1/13/2008 |
| Q: how do you find the distance from (2,1,2) to the orgin of a 3-d figure? A: The answer is not always findable, but the way to do it it have x(t), y(t), and z(t) where t starts ... | |
| I need help desperately!! | 1/12/2008 |
| Q: set=...y^2=x....not a function Give three ways of removing parts of the set, y^2=x, so that the ... A: In most cases, y=ax^2 + bx + c, but here, the x and y values have been reversed. It still follow ... | |
| trigonometry unit circle | 12/16/2007 |
| Q: alright i'm in precal and we're learning about the unit circle and i'm lost.First, what is the unit ... A: Take the unit circle with radius r = 1. sin = opposite or hypoteneuse. The opposite side has ... | |
| Algebra 1 and Calculus | 12/13/2007 |
| Q: I'm having trouble starting out on my algebra questions... Write an equation in slope-intercept ... A: Lines have the form y = mx + b. The variable m denotes the slope and b is for the y intercept. 3. y ... | |
| Calculus again | 12/13/2007 |
| Q: 1)How do I locate extrema on a closed interval? 2) What is differentiability? 3) What is ... A: 1)How do I locate extrema on a closed interval? Solve the derivative for f'(x) = 0 and check the ... | |
Calculus
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