| Subject | Date Asked |
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| Centroid: | 10/2/2009 |
Q: from triangle shown we have to find the ratio between AF,BF using vectors only the line segments ...
A: AF = BF , so the ratio is 1 To simplify the calculations , we may assume that C is the origin , C = ...
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| Applications of integration... | 10/1/2009 |
Q: The question is: Find the volume of a pyramid with height (h) and with a base of an equilateral ...
A: Use integration to "sum up" cross section areas to find the volume. A horizontal plane cross section ...
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| line integral | 10/1/2009 |
Q: determine wheter the force F is conservative by finding the value of the line integral F.dx for ...
A: The notation I use might be different from yours , but here it is dx,dy stand for the derivatives ...
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| ap calculus preparation | 9/30/2009 |
Q: 32. For question 32, find the standard equation of the circle satisfying the given conditions. A ...
A: For the standard equation of a circle you need to find the center and radius The midpoint of a ...
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| math | 9/30/2009 |
Q: what are to rules to rationlizing any futions and/or derivitives
A: I assume you are talking about fractions with a binomial in the denominator that has a square root ...
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| Proof of sum/subtraction laws | 8/27/2009 |
Q: I am currently studying the precise definition of limits. As to the Proof of Sum Law, I am unsure ...
A: I assume you are trying to show that the limit of the sum of two functions ,f and g , will be the ...
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| limits | 4/21/2009 |
Q: Let f(x)= |2 + 9 x| a)Then for x < -2/9, f'(x)=. b)The left-hand derivative of f(x) at x= -2/9 is ...
A: The difficulty is caused by the fact that there is no rule for finding the derivative of |2 + 9 x| ...
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| Calc. | 4/21/2009 |
Q: I have a piecewise function: f(x) (-6x^2+4x for x<0 (3x^2-2 for x > or equal to 0 and ...
A: The function you have defined is neither continuous nor differentiable at 0. The limit for f(x) as ...
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| Min/Max problems | 3/22/2009 |
Q: A rectangular box with square base and top is to be made to contain 1250 cubic feet. The material ...
A: Let x be the length in feet of the edges of the box on the top and bottom. Let y be the height of ...
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| Integration | 2/21/2009 |
Q: Is my integration correct: F= 2pg∫10√(4-x^2)dx F=20pg∫√(4-x^2)dx let ...
A: You left out some factors Let x = 2sinθ dx = 2cosθ dθ F = ...
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| 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) I must use "t" instead of the greek letter theta (27cost)^2 / 27^2 + y^2 = 1 (cos(t))^2 + y^2 ...
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| Calculus | 1/22/2009 |
Q: You are the marketing vice president of the bamboo pen tablets company, and you forecast that the ...
A: a) R(p) = (p)(-0.5p + 140) = -0.5p^2 + 140p b) Sorry, I can't send you a graph :( It will ...
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| help. need asap. | 1/21/2009 |
Q: Evaluate all six trigonometric functions at t, where the given point lies on the terminal side of an ...
A: If (x,y) are the coordinates of a point on the terminal side of an angle t , then sin(t) = y / (x^2 ...
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| Calc | 1/21/2009 |
Q: a baseball diamond is a square with each side 90 feer in length a player runs from second base to ...
A: Unfortunately , I can't draw a diagram for you ,and you really need to see one to fully understand ...
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| integrals | 4/21/2008 |
Q: The rate at which water is sprayed on a field of vegetables is given by R(t)=2 times the square root ...
A: The average value of the function is the integral divided by the length of the interval. We want ...
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| derivatives | 1/21/2008 |
Q: Let f and g be twice differentiable functions such that f'(x)<=0 for all x in the domain of f. If ...
A: You can't say anything about f,g and h at x = 2 Suppose a , b and c are any numbers and we let ...
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| rates | 10/23/2007 |
Q: I need help with the following problem: A particle P is moving in an xy plane. At any instant t, ...
A: My first answer was nonsense, here is the right way: Distance to the origin is D(t)=(x^2 + y^2)^1/2 ...
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| Calculus help | 10/22/2007 |
Q: A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft. high. if water ...
A: Let r be the radius of the circle of water at the top , h the height or depth of the water and V the ...
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| related rates | 10/21/2007 |
Q: Water is stored in a cone shaped resevoir[vertex down]. Assuming the water evaporates at a rate ...
A: Let r be the radius of the circle of water at the top , h the height or depth of the water and V the ...
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| precalc | 9/21/2007 |
Q: I have a problem that I cannot figure out for the life of me. I don't want the answer, just a hint ...
A: I will use "t" for the angle theta You need to know that sin^2(t) + cos^2(t) = 1 So (-.79)^2 + ...
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| maximum minimum | 6/21/2007 |
Q: a window has the shape of a rectangle surmounted by an isosceles triangle. If the perimeter of the ...
A: I will assume that the length and width of the rectangle are x and y. The area of the triangle is ...
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| math precalculus | 5/16/2007 |
Q: Perhaps youve heard of the famous English pirate named Blackbeard, but did you ever hear about his ...
A: The three men end up at the points (11,-2) , (9,6) and (1,-2) The first string joins the points ...
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| Calculus | 3/15/2007 |
Q: You have a rectangle that has a perimeter of 91 feet. The length is 8 more than twice the width. ...
A: Let L = length W = width The length is 8 more than twice the width L = 2W + 8 perimeter of 91 ...
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| exponential derivatives | 1/15/2007 |
Q: We started doing derivatives of exponential functions, and apparently when you derive, you're going ...
A: For your first question, look at the two functions f(x) = x^2 and g(x) = 2^x , do you see what is ...
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| optimization | 12/11/2006 |
Q: Courtney is hiring people to build her a pig pen. She has 150 feet of fencing to use. What ...
A: I assume the pen is to be a rectangle. Let L be the length and let W be the width. Then the ...
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| calculus | 12/11/2006 |
Q: A given function is f:R to R -f is 3 times diffrentiable. -f(x), f'(x) ,f''(x) and f'''(x) are all ...
A: This is problem B4 from the 1999 Putnam Exam. There are at least three different solutions available ...
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| calculus-integral | 12/1/2006 |
Q: How do you solve problems such as the integral from 2 to 4 of x(arc secx)dx? I never understood any ...
A: The important thing to know is that the inverse trig functions have algebraic derivatives, in other ...
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| trig identity question | 11/20/2006 |
Q: This is a problem that has had me stuck for about 4 days now. It's a take home test and it is due ...
A: Just multiply the numerator and denominator of cosx/(1+sinx) by 1-sinx , this gives ...
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| tangent lines | 9/27/2006 |
Q: I was wondering if you could help me with this oneFind the equation of the line(s) that are tangent ...
A: Suppose a line tangent to both curves passes through the points on the curves (a,a^2) and (b,-b^2 + ...
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| Integration/Fund The of Calc | 9/26/2006 |
Q: I am working through a study guide and this one is stumping me. Q: Suppose f is continuous and x^2 ...
A: Since x^2 <= f(x) <= 6 when x is between -1 and 2 , S x^2 dx <= S f(x)dx <= S 6 dx , where the ...
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| Differentiating trig functions | 9/26/2006 |
Q: I am trying to differentiate the following. y = ( cos x + sin x ) / (cos x - sin x) I have to ...
A: From what you have , you can't cancel cosx - sinx from the denominator because it only appears as a ...
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| cal 2 help - integration | 9/17/2006 |
Q: definite integral from 0 - pi/3 tanxsec^3/2dx if you can just get me started, that'd be great. ...
A: You want S (tanx)(secx)^3/2 dx Make the substitution u = secx Then du/dx = (secx)(tanx) dx = du / ...
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| Antidifferentiation | 9/16/2006 |
Q: I a having difficulty with the following problems can you give me some guidance. Thanks. 1. A ...
A: Problem 1) is much more difficult than 2). Unless you are told the form of the function F in ...
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| Calculus | 9/5/2006 |
Q: I am going through a study guide for my calculus midterm on Thursday and I was hoping you could show ...
A: First, find the points of intersection . y = -x^2 and x-4y-18=0 from the second equation, ...
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| Limits with absolute values | 9/3/2006 |
Q: I am trying to find the limit as x approaches 3 from the left. I am stumped due to the absolute ...
A: You are right, the only expression that matters in finding this limit is |x-3|/(x-3) When x ...
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| calculus | 8/24/2006 |
Q: Hey I am doing an integral in diffy q. I was wondering if you could help me with the integral ...
A: You want S 1/(u^2+2u) du Use partial fractions a/u + b/(u+2) = 1/(u)(u+2) = 1/(u^2+2u) get a=1/2 ...
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| Integration | 8/24/2006 |
Q: how do I integrate the function: (1/x^2)sin^3(1/x)cos(1/x)dx I know I have to use substitution ...
A: you want S (1/x^2)sin^3(1/x)cos(1/x)dx let u = sin(1/x) then du/dx = -(1/x^2)cos(1/x) dx = ...
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| Area of Surface of Rev. | 8/7/2006 |
Q: I'm trying to set up the equation y=4-x^2, for x=0 to 2 revolved around the y-axis. The equation i ...
A: S.A. = 2pi S x( 1 + (dy/dx)^2 )^1/2 dx dy/dx = -2x so S.A. = 2pi S x(1+4x^2)^1/2 dx where the ...
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| the intermediate value theorem | 8/6/2006 |
Q: i wanna ask about wht is "IVT"? wht is this theorem for? what is the most important things we need ...
A: The Intermediate Value Theorem tells you about the values of a continuous funtion. If a continuous ...
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| Partial Fraction Decomposition | 8/6/2006 |
Q: I am having trouble with this problem, trying to solve using partial fraction decomposition... ...
A: Set A/(2x+1) + (Bx+C)/(x^2 + 4) = (14x^2 + 6x + 25)/(2x+1)(x^2 + 4) so A(x^2 + 4) + (Bx+C)(2x+1) = ...
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| integration | 8/1/2006 |
Q: How do I go about integrating ln(a^2+x^2)? Can I use integration by parts? I used integration by ...
A: Yes , you can use integration by parts , but it looks like you made a little mistake in applying the ...
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| Integrating w/ partial frac. decomp and subs. | 7/31/2006 |
Q: Integrate (x time sqrt(x^2+3))/(x^2-1)dx. I can get up to u=x^2-1 and then 1/2 integral sqrt(u+4)/u ...
A: If you get stuck, try a different substitution. Let u = (x^2+3)^1/2 du/dx = x(x^2+3)^-1/2 dx = ...
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| inequalities | 7/31/2006 |
Q: I am having a lot of troble in writing a system of inequalities such as this, if you have $2,000 to ...
A: Let t = the amount in telecomunications p = the amount invested in pharmaceuticals the total amount ...
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| Finding Area | 7/27/2006 |
Q: Find the area of the region bounded by the curve y=x(squared) and y=x
A: It is really a good idea to draw the graph of the curve y = x^2 and the line y = x together. I can't ...
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| integration - natural logs | 7/26/2006 |
Q: How do I integrate integral dx/(x+x^.5)? thanks
A: We want S 1/(x+x^.5) dx Let u = x^.5 Then du/dx = .5x^-.5 and dx = 2x^.5 du make this substitution ...
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| When are there no limits (Calc BC Summer assignment) | 7/26/2006 |
Q: Hey, I have oneDescirbe 3 times when a limit does not exist. I know that it does not exist when the ...
A: The third case is when the function oscillates. The value of the function varies by at least a fixed ...
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| pre calc | 7/14/2006 |
Q: Write y=2x^2 - 8x + 3 in the form y = a(x-h)^2 + k. Identify the vertex, axis of symmetry, ...
A: y = 2(x^2 - 4x +3/2) x^2 - 4x + 3/2 = x^2 - 4x + 4 - 5/2 = (x-2)^2 - 5/2 so y = 2((x-2)^2 - 5/2) ...
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| Limits | 5/17/2006 |
Q: x^2 + a if x < -1 If g(x) = x+a^2 if x = -1 a - x ...
A: For the limit to exist, he limit on the left, (x < -1) must be the same as the limit on the right, ...
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| Calculus: Derivative Applications | 5/14/2006 |
Q: If I can please see steps to this as well.... If s(t)=.5t^4-5t^3+12t^2, find velocity when ...
A: You don't take the antiderivative of acceleration , because you are given the position function to ...
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| calculus integrals and substitutions | 3/13/2006 |
Q: evaluate S from 0 to 1 x times the square root of 1-x4 not sure how to write this on a computer? ...
A: You want S x(1 - x^4)^1/2 dx from 0 to 1 First, make the substitution y = x^2 Then dy/dx = 2x and ...
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| taylor series | 11/28/2005 |
Q: I have to write a Taylor series for the function: f(x)=sin3x where c= pi/12 i also have to find ...
A: Correction! I just realized that I omitted the n! term from the denominator of Taylor series. This ...
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| related rates | 11/27/2005 |
Q: Problem: A conical tank above a cylindrical tank with a depth of 12 feet and a diameter of 8 feet is ...
A: a) The volume of a cone is (1/3)(pi)(r^2)(h). The volume of the conical tank is thus ...
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| Definite Double Integrals | 5/28/2005 |
Q: I have tried for hours to figure out how to integrate (evaluate) this problem, can you help me ...
A: An anti derivative for (x/y) + (y/x) with respect to x is (x^2/2y) + ylnx . Evaluate this at x=5 and ...
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| continuity | 5/27/2005 |
Q: Determine the constant “a” and “k” that will make f(x) continuous. ....{2, x<(-1) f(x){ax+k, ...
A: Equating left and right limits at x = -1 , we must have 2 = -a + k Equating left and right limits ...
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| Continuous Functions | 5/27/2005 |
Q: I just have a couple of questions that I need help with. 1. I would like to know how would I prove ...
A: 1) This is easy if you know that the sum and product of continuous functions is continuous. Let ...
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| function. thanks for your help | 1/1/2005 |
Q: Let f be the function given by f(x)=x over the sqare root of x^2-4. a. find the domain of f. b. ...
A: a) The domain is {x| x>2 or x<-2}, so x can be any number greater than 2 or less than -2. This is ...
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| Mean Value Theorem | 7/27/2004 |
Q: I need help solving this problem: Find the sum of the values satisfying the Mean Value Theorem of ...
A: We need all the values for x in the interval between 0 and 4 that satisfy f'(x) = (f(4) - f(0))/ (4 ...
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| Caluculus question | 5/25/2004 |
Q: If dy/dx = x^3 y^2 and x=2 when y=-1 then y=f(x) is?
A: This is a separable differential equation. dy/dx = x^3 y^2 y^-2 dy = x^3 dx Integrate the ...
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| Caluculus (average rates of change) | 2/26/2004 |
Q: I need to calculate the average rate of change for: R(0)= square root of 4x+1 with intervals ...
A: To find the average rate of change , evaluate the function at the endpoints of the interval, then ...
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| Derivatives of e^x and ln e | 2/26/2004 |
Q: My question regards the different results obtained in textbooks when one finds the derivative of e ...
A: Well , your textbook seems to be confusing you on a simple proof. Here is the argument, Let y = ...
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| Improper Integrals | 2/25/2004 |
Q: (x^3)x(cos(x^2)dx
A: To find S (x^3)(cos(x^2)) dx , let u = x^2. Then du/dx = 2x and dx = du/2x. S(x^3)(cos(x^2)) dx = ...
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| length of curve | 1/24/2004 |
Q: I know this is easy but its stumping me. My book has the answer as 6+ln(2) but I can't see how its ...
A: I really can't give a specific reference to prepare for the GRE. I remember when I took it , I went ...
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