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Calculus/Questions Answered by Expert Frederick Koh
| Subject | Date Asked |
| calculus 2 | 4/23/2012 |
| Q: which of the series converges or diverges? a) (n=1 to n=oo) 1/(10n+3) b) (n=1 to n=oo) ... A: Both series would converge; for (a) when n tend to infinity, the denominator becomes infinitely ... | |
| Pre-Calculus | 4/21/2012 |
| Q: "A ball is dropped from a height of 132 feet. After each bounce, the ball rebounds one third of the ... A: The exponential decay description is an inappropriate model. The distance travelled by the ball ... | |
| Limited growth bus calc | 4/12/2012 |
| Q: How do u solve the limited growth equation for exponential growth law of dy/dt= k(m-y). I know the ... A: dy/dt= k(m-y) 1/(m-y)*dy/dt = k Integrating both sides wrt t, Int 1/(m-y)dy = Int k dt ... | |
| Calculus question | 4/7/2012 |
| Q: (b) Using (a) or otherwise, express 12 sin^3 x + 2 cos(3x) - 9 sin x + sin(3x) as a single ... A: As to how I got sin^3 x = 1/4 [ 3 sin x - sin(3x)], I am merely manipulating the answer in part ... | |
| Partial differentiation | 4/6/2012 |
| Q: Sir, Signs: d= derivative dho=partial derivative I have 2 functions A=A(x,y) and B=B(x,y). x and y ... A: You need to modify your answer. Firstly, we seek out the separate total differentials of A and B: ... | |
| Calculus question | 4/5/2012 |
| Q: (b) Using (a) or otherwise, express 12 sin^3 x + 2 cos(3x) - 9 sin x + sin(3x) as a single ... A: sin(3x) = 3 sin x - 4 sin^3 x =======> sin^3 x = 1/4 [ 3 sin x - sin(3x)] For (b), 12 sin^3 x + ... | |
| Calculus | 4/3/2012 |
| Q: what is the limit as x approaches 0 of 1-cos squared of 2x all over x squared A: [cos(2x)]^2 =( 1 - 2(sinx)^2 )^2 = 1- 4( sin x)^2 + 4(sin x)^4-------------(1) ... | |
| Implicit diffentiation | 3/14/2012 |
| Q: Use implicit differentiation to find dy/dx cos(y^2) + x = e^y Heres my attempt.. d/dx[cos(y(x))] ... A: The right hand side of your workings should involve implicit differentiation, hence you need to ... | |
| calculus | 3/7/2012 |
| Q: please can you find the lim LIM ( e^x -cos(x) -2x)/(x^2-2x) as x->0 A: When x is small, e^x-cos(x)-2x is approximately defined algebraically by (1+x+x^2/2)-(1-x^2 /2 ) ... | |
| integration | 2/27/2012 |
| Q: sir, how to integrate the following problem finding it difficult to integrate INTEGRATE LN ... A: Let 2^t =u, then differentiating both sides wrt t gives ln2 * 2^t dt= du =====> dt = 1/(uln2) *du ... | |
| Logistic growth | 2/21/2012 |
| Q: A population currently numbers 4000 and is expected to experience logistic growth with a maximum ... A: Let the growth model be x = AB / [ B + (A-B)* e^ (-Ct) ], where A, B and C are real constants. ... | |
| Calculus | 2/14/2012 |
| Q: Find the point on the graph of y=lnx-x that lies closest to the origin A: Distance a of any point from the graph of y=lnx-x to the origin is given by sqrt ( y^2 +x^2) , ie ... | |
| vector | 2/13/2012 |
| Q: The force on an object is F = -18j For the vector v = i-3j, find a) the component of F parallel to v ... A: Assuming your answer to (a) is correct, your answer to (b) is definitely correct. By vector ... | |
| Definite Integration | 2/8/2012 |
| 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 ... | |
| Pre-calc question | 2/5/2012 |
| 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 ... | |
| Math Help | 2/5/2012 |
| 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 ... | |
| Calculus | 1/30/2012 |
| 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 ... | |
| Calculus | 1/16/2012 |
| 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 ... | |
| integrals | 1/12/2012 |
| 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 |
| 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: derivatives for trigonometry | 12/21/2011 |
| 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: derivatives for trigonometry | 12/21/2011 |
| 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 |
| 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 ... | |
| Calculus work | 12/14/2011 |
| 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 ... | |
| derivatives | 12/12/2011 |
| 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 |
| 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 ... | |
| Inequality Problem | 12/7/2011 |
| 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 ... | |
| Verify trig idenities | 12/6/2011 |
| 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) ... | |
Calculus
Answers by Expert:
Frederick Koh
Top Expert on this page
Expertise
I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.
Experience
3 years helping out in a singaporean youth forum: http://forums.sgclub.com/math_help/ (under the moniker whitecorp)
You can also visit my main maths website http://www.whitegroupmaths.com where I have
designed "question locker" vaults to store tons of fully worked math problems.
Peace.
Organizations
IEEE(Institute of Electrical and Electronics Engineers )
Education/Credentials
Former straight As A level student from HCJC (aka HCI); scored distinctions
in both C and Further Mathematics
B Eng (Hons) From The National University Of Singapore (NUS)
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