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| Subject | Date Asked | Expert |
| derivatives for trigonometry | 12/21/2011 | Paul Klarreich |
| Q: show that the curves y=e^-x and y=(e^-x)cosx are tangent to each other at each intersection point. ... A: Questioner:humaira Country:Ontario, Canada Category:Calculus Private:No Subject:calculus: ... | ||
| trigonometric functions | 12/21/2011 | Paul Klarreich |
| Q: i tried to find the x values for this, i got a and c from this question but i didnt get these two. ... A: Questioner:humaira Country:Ontario, Canada Category:Calculus private:No Subject:calculus: ... | ||
| calculus: derivatives for trigonometry | 12/21/2011 | Frederick Koh |
| Q: the normals to the curve y=cos2x at the points A(pi/4,0) and B(3pi/4,0) meet at the point C. find ... A: y=cos2x Differentiating both sides wrt x gives dy/dx=-2sin2x Gradient function of the normal at ... | ||
| calculus | 12/21/2011 | Scotto |
| Q: find the coordinates of the points on the curve y=2-cosx/sinx in the range 0<x<2pi where the ... A: If the curve is y = 2 - cosx/sinx, then that is y = 2 - ctnx. However, I believe it really to be y ... | ||
| calculus: derivatives for trigonometry | 12/21/2011 | Frederick Koh |
| Q: given that y= 1/cosx + 1/sinx show that dy/dx= sin^3x-cos^3x/(sin^2xcos^2x) ANSWER: y= 1/cosx + ... A: If the gradient is 0, then dy/dx=0 (sin^3 x - cos^3 x)/(sin^2 x cos^2 x) =0 ie sin^3 x - cos^3 x ... | ||
| calculus: derivatives for trigonometry | 12/21/2011 | Frederick Koh |
| Q: given that y= 1/cosx + 1/sinx show that dy/dx= sin^3x-cos^3x/(sin^2xcos^2x) A: y= 1/cosx + 1/sinx = sec x + cosec x Differentiating both sides wrt x gives dy/dx = (sec x) (tan ... | ||
| Quotient Rule | 12/17/2011 | Scotto |
| Q: I've been given the function f(x)=x^(2/3)(x-5) and by using product rule came up with the first ... A: Since we have f'(x) = g(x)/h(x), we know that f"(x) = [h(x)g'(x) - g(x)h'(x)]/h˛(x). Since g(x) = ... | ||
| Trigonometric equation. | 12/15/2011 | Paul Klarreich |
| Q: I'm hoping you'll be able to help me out with some problems... The questions states: solve for all ... A: Questioner: Mike Country: Ontario, Canada Category: Calculus Private: No Subject: TRIG ... | ||
| Centroid | 12/14/2011 | Paul Klarreich |
| Q: A triangular trough has a base of 3 feet height of 3 feet and a length of 10 feet if the trough is ... A: Questioner: christopher deblasio Country: New York, United States Category: Calculus Private: No ... | ||
| Calculus work | 12/14/2011 | Frederick Koh |
| Q: Suppose 2 Nm of work is needed to stretch a spring from its natural length of 0.3m to a length of ... A: Potential energy stored in a spring when stretched by x m = (1/2)k x^2, where k is the spring ... | ||
| calculus | 12/14/2011 | Scotto |
| Q: suppose a spring has a natural length of 8 inches to extend the spring 2 inches a force of 3 pounds ... A: It is known that for springs, E = FK, where ... E is the displacement, and that is 2", F is the ... | ||
| derivatives | 12/12/2011 | Frederick Koh |
| Q: Find the derivative of ln[ln(x^2)^5]. Please show steps. Thanks! ANSWER: Firstly, we will try to ... A: Sure. Here goes: ln{[ln(x^2)]^5} = 5 ln [ln(x^2)] (Note that I pushed the 5 all the way to the ... | ||
| derivatives | 12/12/2011 | Frederick Koh |
| Q: Find the derivative of ln[ln(x^2)^5]. Please show steps. Thanks! ANSWER: Firstly, we will try to ... A: If your solution manual states that 5/(xlnx) is the answer, the only way you are going to get that ... | ||
| Trigonometric limit | 12/11/2011 | Paul Klarreich |
| Q: how can we prove lim sinx= sina when x approach to a A: Questioner: bektur Country: Istanbul, Turkey Category: Calculus Private: Yes <<<< changed ... | ||
| Related Rates | 12/10/2011 | Paul Klarreich |
| Q: I've looked through your previously worked related rates problem, but I'm still having a little ... A: Questioner: Renee Country: Indiana, United States Category: Calculus Private: No Subject: ... | ||
| Wrong answer - revision posted. | 12/8/2011 | Paul Klarreich |
| Q: Your answer to part b at http://en.allexperts.com/q/Calculus-2063/Related-rates-geometry.htm is ... A: It took a while to figure out what was wrong, but I see it now. It also took about 3 minutes just to ... | ||
| Difference Equations | 12/7/2011 | Paul Klarreich |
| Q: My calculus professor is kind of in his old world and just creates problems out of the blue. If you ... A: Questioner: Austin Country: Iowa, United States Category: Calculus Private: No Subject: Calculus ... | ||
| Inequality Problem | 12/7/2011 | Frederick Koh |
| Q: Your company needs to temporarily hire a programmer to work on a project. Two proposed payment ... A: Let the amount incurred by a particular plan be $ y , and the number of hours worked be x. For Plan ... | ||
| Basic functions | 12/7/2011 | Paul Klarreich |
| Q: a.Program speed, or runtime, is an important concept in computer programming, and it is measured in ... A: Questioner: Patti Country: Texas, United States Category: Calculus Private: No Subject: How Do ... | ||
| Continuity | 12/7/2011 | Paul Klarreich |
| Q: Prove that 2π+x+2πsinx = 0 has at least two solutions on [-π,0]. I'm a bit stumped. A: Questioner: Granit Country: Ontario, Canada Category: Calculus Private: No Subject: Calc. Rolles ... | ||
| Logarithmic functions | 12/6/2011 | Paul Klarreich |
| Q: a.One important application of logarithms is found in various computer search routines. For example, ... A: Questioner: Patti Country: Texas, United States Category: Calculus Private: No Subject: ... | ||
| An inequality question | 12/6/2011 | Ahmed Salami |
| Q: Your company needs to temporarily hire a programmer to work on a project. Two proposed payment ... A: In the first scheme, the pay in dollars <b>P1</b>= 1000 + 20<b>h</b> where <b>h</b> is the number of ... | ||
| Verify trig idenities | 12/6/2011 | Frederick Koh |
| Q: Please help me on the problems. cos(x)sec(x)-cos^2(x)=sin^2(x) (sin^2(x))(1+cot^2(x))=1 ... A: cos(x) sec (x) -cos^2(x) =cos(x)* 1/ cos(x)- cos^2(x) =1 - cos^2(x) =sin^2 (X) (shown) ... | ||
| Implicit Differentiation | 12/3/2011 | Scotto |
| Q: Could you please help me solve tan(xy)=xy with implicit differentiation? I got the derivative: ... A: What is left to do is solve for dy/dx. That is, we have sec˛(xy)y + sec˛(xy)(dy/dx) = y + x(dy/dx). ... | ||
| Rate of Change of The Volume of A Cone | 12/2/2011 | Socrates |
| 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 | 11/30/2011 | Scotto |
| Q: Find the equation of the slant asymptote for the function, f(x)=(x^2+1)/(x+1) A: I somehow didn't remember what an assymptote was until now. I believe the slope is undefined since ... | ||
| Maximum-minimum problems | 11/28/2011 | Paul Klarreich |
| Q: A building with a rectangular base is to be constructed on a lot in the form of a right triangle ... A: Questioner: rachel Country: Manila, Philippines Category: Calculus Private: No Subject: ... | ||
| Calculus, Find Integral | 11/28/2011 | Socrates |
| 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 ... | ||
| Velocity and acceleration. | 11/26/2011 | Paul Klarreich |
| Q: A small frictionless cart, attached to the wall by a spring is pulled 10 cm from its rest position ... A: Questioner: Joshua Country: California, United States Category: Calculus Private: No Subject: ... | ||
| Convexity and increasing character | 11/25/2011 | Scotto |
| Q: I am an Italian boy with a school and university curriculum in humanities, who is trying to ... A: -f is strictly convex if and only if f' is strictly increasing; Note that f'(x) is also the slope ... | ||
| calculus | 11/24/2011 | Ahmed Salami |
| Q: a]Express f(x)=x^2-6x+14 in the form f(x)=(x-h)^2+k,where h and k are to be determined. b] Hence, ... A: For a quadratic form x˛ + kx, we complete the square by adding (k/2)˛ and then factorising as (x - ... | ||
| calculus | 11/24/2011 | Scotto |
| Q: The following diagram below shows part of the graph of f(x)=5-x^2 with vertex V(0,5). Its image ... A: The vertex is currently at (0,5). To shift the vertex to (3,6), note that the change is x is from 0 ... | ||
| Polynomials | 11/24/2011 | Paul Klarreich |
| Q: Part of the graph of f(x)=(x-p)(x-q) is shown below.[in pic attached]. The Vertex is at C. The graph ... A: Questioner: kevin Country: Beijing, China Category: Calculus Private: No Subject: calculusPart ... | ||
| How to Buy Stocks on a Foreign Stock Exchange | 11/24/2011 | mervyn |
| Q: 1. Which are the Online Brokerages in India which will allow me to purchase stocks listed on foreign ... A: as you know mital steel bought iscor in SA. and now monopolizes the steel industry here. In fact ... | ||
| Integral Question | 11/24/2011 | Socrates |
| 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 . ... | ||
| Completing the square, | 11/23/2011 | Paul Klarreich |
| Q: consider the function f(x)=2x^2-8x+5. a)express f(x) in the form of a(x-p)^2+q,where a,p,q are Z? ... A: Questioner: kevin Country: Beijing, China Category: Calculus Private: No Subject: ... | ||
| How to Buy Stocks on a Foreign Stock Exchange | 11/23/2011 | mervyn |
| Q: 1. Which are the Online Brokerages in India which will allow me to purchase stocks listed on foreign ... A: It looks like Capitalism is on the verge of a major and total collapse. Read the rest of the answer ... | ||
| Boomerang - Laws of Physics and Geometrical Shape | 11/21/2011 | mervyn |
| Q: http://en.wikipedia.org/wiki/Boomerang How does a Boomerang and Returning Boomerang works ? What ... A: From chapter 3 of the site on your question. Continuum mechanics involves cartesian tensors, of ... | ||
| Archery Variation Sport (angular Velocity) | 11/21/2011 | mervyn |
| Q: Do you feel this variation of Archery game can be introduced as a Good Olympics Sport in future ? ... A: You should patent this idea. Using numerical control programming a mechanical engineering firm could ... | ||
| Archery Variation Sport (angular Velocity) | 11/21/2011 | mervyn |
| Q: Do you feel this variation of Archery game can be introduced as a Good Olympics Sport in future ? ... A: A reflecting pool of water causes diffraction which would have to be corrected for by the archer ... | ||
Calculus
Answers by Expert:
Paul Klarreich
Top Expert on this page
Expertise
All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience
I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
Education/Credentials
(See above.)
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