| Subject | Date Asked |
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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). ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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'. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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), ...
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| 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 + ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) ...
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| 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. ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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", ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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). ...
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| "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 ...
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| 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, ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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). ...
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| 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. ...
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| 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 = ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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: ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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). ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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- ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 + ...
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| 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 ...
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| 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 ...
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| 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). ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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) ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 + ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 = ...
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| 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 ...
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| 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 ...
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| 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, ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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. ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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)) ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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| 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 ...
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