# CAS MA 124 Study Guide - Midterm Guide: Improper Integral, Absolute Convergence

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Professor MA 124 - Spring ’10 - Exam 2 - Prof. Meuser
1) (13 points) Consider the deﬁnite integral
Z0
2
1
x+ 2 dx
b) Determine whether this integral converges or diverges. Explain your answer using
properties of integrals and limits.
2) (14 points) Determine whether the improper integral
Z
0
xexdx
converges or diverges. Write any necessary limits or theorems needed to determine your
answer. For any limits you are ﬁnding, explain why those limits exist or do not exist using
properties of limits.
3) (14 points) Determine whether the following sequences converge or diverge. If they
a)an= (1)nn
(n+ 1)2b)an=n2en
4) (14 points ) Consider the number
0.73 = 0.73737373 · · ·
a) Write this number in terms of a geometric series.
b) Does this geometric series converge or diverge ? Explain your answer.
c) If this geometric series converges ﬁnd it’s sum.
c) Express this number as a ratio of integers, i.e. as a fraction a/b for integers aand b.
5) (13 points) Determine whether the following series converges or diverges
X
n=1
nen
6) (13 points) Determine whether the following series converges or diverges
X
n=1
n3
n41
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