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Calculus/Questions
| Subject | Date Asked | Expert |
| Applications of derivative | 2/8/2012 | Paul Klarreich |
| Q: a) find an equation in slope-intercept form of the tangent line to the parabola y= (x-1)^2 +2 at the ... A: Questioner:Tommy Country:North Carolina, United States Category:Calculus Private:No Subject:calculus ... | ||
| Definite Integration | 2/8/2012 | Frederick Koh |
| Q: I need to find the definite integral on the interval (0,5) of |3(x^2)-8(x)|. I divided it into the ... A: Firstly, your final answer should be 43.96, not 49.6 (I have verified this using a graphic ... | ||
| Piecewise function. | 2/5/2012 | Paul Klarreich |
| Q: Can you help me with (b) and (c) of the following question? The price of an item is initially $700. ... A: Questioner:Erin Subject: Piecewise function.Can you help me with (b) and (c) of the following ... | ||
| Pre-calc question | 2/5/2012 | Frederick Koh |
| Q: Can you help me with (b) and (c) of this question? The price of an item is initially $700. For the ... A: In the 4th year, the price becomes 700+30(4)=820 When 4 < t 9, P(t)= 820 -30(t-4)= 820 - 30t +120 ... | ||
| Pre-Calc question | 2/5/2012 | Scotto |
| Q: Can you help me with parts (b) and (c) of the following question? The price of an item is initially ... A: a) After 4 years, the value will have gone up by $120, so it will be worth $820. To get an equation, ... | ||
| Math Help | 2/5/2012 | Frederick Koh |
| Q: Suppose u(x,t) = f(x+at) + g(x-at), where a is constant and f & g are twice differentiable functions ... A: It is with respect to t; in this case you are partial differentiating wrt t and treating x as the ... | ||
| Domain and Range | 2/3/2012 | Paul Klarreich |
| Q: Consider the following equation: f(x) = -4√x + 1. (-4 times square root of x, plus 1) 1. What ... A: Questioner:Hiral Country:New Jersey, United States Category:Calculus Private:Yes ... | ||
| max/min question | 2/2/2012 | Paul Klarreich |
| Q: A lamp is hung above a circular table of radius r=15in at a variable height h. As h varies, the ... A: Questioner:Alexis Country:Wisconsin, United States Category:Calculus Private:No Subject:max/min ... | ||
| Domain | 2/1/2012 | Paul Klarreich |
| Q: What is the domain of the following in interval notation? (square root of 5x-2) / (x^2-4). I think ... A: Questioner:Hiral Country:New Jersey, United States Category:Calculus Private:Yes ... | ||
| Pre-Calculus I | 2/1/2012 | Paul Klarreich |
| Q: Mr. Klarreich, I have a question regarding one of your past answers, at ... A: Questioner:Matt Country:Nevada, United States Category:Calculus Private:No Subject:Pre-Calculus IMr. ... | ||
| Transformations in Graphs | 2/1/2012 | Paul Klarreich |
| Q: What transformations occur in: 2(-3x)^3 - 7? I think it's a reflection in the y-axis, 7 units ... A: Questioner:Hiral Country:New Jersey, United States Category:Calculus Private:Yes <<<<<<<<<<<<< ... | ||
| calculus question | 1/31/2012 | Scotto |
| Q: wondering if you could help me with this question, PART A). Find 5 nonzero terms of Fourier Series ... A: Yes, the attached graph made the 1st answer very clear. PART A By looking at the graph, non-zero ... | ||
| Algorithm | 1/31/2012 | Scotto |
| Q: Instructions: Given the gallons of gasoline used and the starting miles and the ending miles, ... A: starting mileage 1200 ending mileage 1290 gallons used 6 mileage = (end - start)/used = ... | ||
| Limit proofs | 1/30/2012 | Paul Klarreich |
| Q: I would like to seek your advice to solve this problem: Prove, using epsilon-delta definition, ... A: lim[x->a] x^1/3 = a^1/3 Let y = x^1/3, b = a^1/3 Show that given e [epsilon], we can find d ... | ||
| Calculus | 1/30/2012 | Frederick Koh |
| Q: I'm from NUS too & currently in Year 1. I would like to seek your advice to solve this problem: ... A: The essence of epsilon-delta is to obtain a relationship between epsilon and delta themselves. If ... | ||
| Limit proof | 1/25/2012 | Paul Klarreich |
| Q: May I know how to prove, using epsilon-delta definition, that limit of sin(1/x) does not exist as x ... A: Questioner:Alfredo Country:Singapore Hi Sir, May I know how to prove, using epsilon-delta ... | ||
| Applications of derivative | 1/20/2012 | Paul Klarreich |
| Q: MyFind the equation of the line tangent to the graph of y = x^3 + x ^2 + 2 at its point of ... A: Questioner:Taalib Country:Virginia, United States Category:Calculus Private:No ... | ||
| Calculus | 1/19/2012 | Socrates |
| 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 ... | ||
| Calculus | 1/16/2012 | Frederick Koh |
| Q: What would be the volume of the largest right circular cone that can be inscribed inside a sphere ... A: Firstly, recognize that the vertices of the cone must be in contact with the sphere's interior. Let ... | ||
| Maximum-minimum problem | 1/15/2012 | Paul Klarreich |
| Q: Suppose you work on a ranch. The rancher tells you to build a circular fence around a 100 yard ... A: Questioner:Mary Country:Massachusetts, United States Category:Calculus Private:No Subject:calculus ... | ||
| integrals | 1/12/2012 | Frederick Koh |
| Q: Calculate the area bounded by the curve y=16/x^2, the line x=4 and the line y=16. I know how to do ... A: I have provided a diagram for you to see things in a clearer manner: <a ... | ||
| calculus | 1/11/2012 | Frederick Koh |
| Q: intregrate e^(-x^2) from -infinity to infinity.and visualise it under dirac delta function. A: Let I be the definite integral of e^(-x^2) wrt x from 0 to infinity. ie I = Int (0 to infinity) ... | ||
| Calculus | 1/5/2012 | Scotto |
| Q: Suppose r(x)=x^2/(x^2+1) represents revenue and c(x)= (x-1)^3/3-1/3 represents cost, with x measured ... A: Since profit is revenue minus cost, we have p(x) = r(x) - c(x) = [x²/(x²+1)] - [(x-1)³/3 - 1/3]. At ... | ||
| Calculus - Comparing Related Rates | 1/4/2012 | Abe Mantell |
| Q: Part of a circuit has two resistors connected in parallel. R1 is a constant resistor of 10 ohm, ... A: In this case, I would solve for R in terms of R1 and R2, then differentiate with respect to t. ... | ||
| trigonometric functions | 12/22/2011 | Paul Klarreich |
| Q: differentiate y=5x^2 tan^3(3x^2-1) A: Questioner:humaira Country:Ontario, Canada Category:Calculus Private:No Subject:calculus: ... | ||
| 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)]/h²(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: ... | ||
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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