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Unformatted text preview: Name:
TA: PID:
Sec. No: Sec. Time: Math 20B.
Midterm Exam 2
February 27, 2008 Turn oﬀ and put away your cell phone.
No calculators or any other devices are allowed on this exam.
You may use one page of notes, but no books or other assistance on this exam.
Read each question carefully, answer each question completely, and show all of your work.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clariﬁcation.
1. (4 points) Find the 3 cube roots of −8i. You may leave the result in polar form. #
1
2
3
4
Σ Points
4
4
8
8
24 Score 2. (4 points) Does the improper integral
1
0 x4 1
√ dx
+2 x converge or diverge? You do not need to evaluate the integral; however, you must
provide a correct reason to earn credit. 3. (a) (4 points) Find the partial fraction expansion (PFE) for (b) (4 points) Use your PFE found in part (a) to evaluate 3x2 − 9x + 13
.
(x − 3)(x2 + 4) 3x2 − 9x + 13
dx.
(x − 3)(x2 + 4) eax
x eax
− 2 + C using
4. (a) (2 points) Derive the integration formula
x e dx =
a
a
integration by parts. Be sure to show your work.
ax (b) (6 points) The formula veriﬁed in part (a) is also valid when the constant a is a
complex number. Use this fact to evaluate
x e2x cos(2x) dx
using complex exponentials. You may leave complex exponentials in your answer. ...
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This note was uploaded on 08/31/2011 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.
 Winter '08
 Justin
 Math, Calculus

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