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Calculus/Questions Answered by Expert Socrates
| Subject | Date Asked |
| Calculus | 1/19/2012 |
| Q: How do you solve: max of f(x)=-4sqrt 2-x ? A: This is not really a calculus problem. Observe that -4√(2-x) is always less than or equal to ... | |
| Rate of Change of The Volume of A Cone | 12/2/2011 |
| Q: The amount of water evaporating from a conical container varies directly with the exposed surface ... A: Let E(a) be the rate of evaporation when the surface area of the circular region on top is a. We are ... | |
| Calculus, Find Integral | 11/28/2011 |
| Q: I'm asking about this equation, i hardly do it, my papers are all sketch of it, but still.. no ... A: You want to find S |x|x^2 dx from -1 to 1 and S |x|[sin(x)]^3 / [1+cos(x)] dx from -1 to 1 ... | |
| Integral Question | 11/24/2011 |
| Q: If F(x) is continuous and the integral of f(x) from 0 to 4 = 10 then compute the integral of f(2x) ... A: S f(x) dx from 0 to 4 is 10. Make the change of variables x=2y , then dx/dy = 2 and dx = 2 dy . ... | |
| limits | 5/19/2011 |
| Q: Evaluate the given limit in the image A: Evaluate the natural log of this limit , then raise e to your answer. ln[(x^2+5x+6)/(x^2+2x+3)]^x ... | |
| function | 1/17/2011 |
| Q: Let f(x) = x/x-5. Find a function y = g(x) so that (f o g)(x) = 3x. g(x) = ? A: f(g(x)) = 3x f(g(x)) = g(x)/(g(x)-5) So g(x)/(g(x)-5) = 3x g(x) = (3x)(g(x)-5) g(x) = 3xg(x) - ... | |
| Calculus | 10/27/2010 |
| Q: Find the rate of change of the surface area of a sphere when the radius is 3ft and the rate of the ... A: A(r) = 4πr^2 the radius , r , is a function of time, t , so the radius is r(t) A(t) = ... | |
| Calculus | 7/26/2010 |
| Q: Find the solution of dy/dx= ((y/(1-x^2)) which passes through (0,1). Write the solution explicitly ... A: use separation of variables dy/dx = y/(1-x^2) (1/y)dy = 1/(1-x^2) dx S (1/y)dy = S 1/(1-x^2) dx ... | |
| calculus proof | 4/7/2010 |
| Q: I need a step by step proof of (sin^-1(x)=((1-x^2)^(-1/2)or (sin^-1(x)= 1/(1-x^2)^(1/2) A: I assume you want the derivative of sin^-1(x) We know that sin(sin^-1(x)) = x Take the derivative ... | |
| Calculus | 4/6/2010 |
| Q: Let f be a function whose derivative is given by f'(x)=(x/15)+sin(e^.2x) how many relative maximum ... A: Sorry for the delay. There are two relative maximum points for f(x). At approximately x=6.36 and ... | |
| Calculus 2 - Fluid Forces | 3/2/2010 |
| Q: A swimming pool is 5 feet deep at one end and 10 feet deep at the other, and the bottom is an ... A: You will need to draw some pictures for this . The pool has 4 sides . Two sides are rectangles. One ... | |
| Applications of Derivatives | 12/30/2009 |
| Q: The power P (watts) of an electric circuit is related to the circuit's resistance R (ohms) and ... A: Think of P , R and I as functions of t and use the rules for finding the derivatives of products and ... | |
| Calculus | 12/30/2009 |
| Q: A juice can in the shape of a right circular cylinder has a fixed capacity. If the material used for ... A: Let the height of the can be h and let the radius be r. To find the cost of the can , we need the ... | |
| Applied Max/Min | 12/3/2009 |
| Q: The strength of a rectangular beam is directly proportional to the product of its width and the ... A: Draw a picture of a rectangle inscribed in a circle of radius 14. Suppose the width is x inches, ... | |
| interals | 12/3/2009 |
| Q: Suppose a particle is observed moving along a straight line, and suppose that the velocity "v" of ... A: a) since velocity is v(t) = 2sin(tπ) , position is p(t) = (-2/π)cos(tπ), the anti ... | |
| Calculus I | 12/2/2009 |
| Q: The function g(x)=x^2 + 1/x is a) concave up over (- infinity, 0) and concave down over (0, ... A: g(x)= x^2 + 1/x g'(x) = 2x - 1/x^2 g''(x) = 2 + 2/x^3 To answer this question, we need to know ... | |
| trignometry | 12/2/2009 |
| Q: i am having a problem solving these trigs. please could you help for my exam 1. prove that tanA+ ... A: 1) tanA + cot A = sinA/cosA + cosA/sinA = (common denominator is sinAcosA) (sinA)^2/sinAcosA + ... | |
| Pre Calc, optimization | 12/1/2009 |
| Q: Can you help please? Minimize the area of a right triangle in quadrant one (nested in the origin). ... A: Let's suppose the line passes through (t,0) on the x axis. So the base of the triangle has length t. ... | |
| calculus | 11/30/2009 |
| Q: find the area of the largest rectangle that can be inscribed in the region bounded by the x-axis, ... A: You really need to draw a picture to understand this, but here is the solution anyway. The vertex ... | |
| 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 = ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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| ... | |
| 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 ... | |
| 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 ... | |
| 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 = ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 + ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 + ... | |
| 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 ... | |
| 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 ... | |
| 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 / ... | |
| 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 ... | |
| 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, ... | |
| 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 ... | |
| 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 ... | |
| 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 = ... | |
| 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 ... | |
| 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 ... | |
| 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) = ... | |
| 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 ... | |
| 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 = ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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) ... | |
| 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, ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 ... | |
| 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 = ... | |
| 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 = ... | |
| 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 ... | |
Calculus
Answers by Expert:
Socrates
Top Expert on this page
Expertise
I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.
Experience
Ph.D. in Mathematics and many years teaching Calculus at state universities.
Education/Credentials
B.S. , M.S. , Ph.D.
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