Name:
Math 106A: Fall 2011
Exam 2: November 4
Version 2
Write all your answers in your exam book. Label problems clearly and circle final answers. Put your name
on your exam and turn it in with your exam book. For full credit you must show your work. Good Luck!
1. (10 points each) Evaluate each of the following integrals.
(a) Zdx
(x+ 2)(x−3)
(b) Zsec4xtan4x dx
(c) Zln x
x3/2dx
(d) Zx2
√9−x2dx
2. (10 points each) Evaluate each of the following definite integrals.
(a) Z1
0
5x+ 2
x2+ 1 dx
(b) Z1
0
dx
√1−x
3. (10 points) Solve the initial value problem (IVP):
y0=x
y, y(2) = 3,(assume y > 0).
4. (10 points) Use a comparison to determine if the following integral converges or diverges. Justify all
claims. Z∞
π
x2
−1
x4+xdx
5. (20 points)
(a) Find P3(x)the third order Taylor Polynomial of f(x) = 1
√xbased at x0= 4.
(b) Use your answer in (a) to estimate 1
√5to 7 decimal places.
(c) Use Taylor’s Theorem to calculate the maximum possible approximation error committed by
P3(x)on the interval [3,6].