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

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10 Oct 2018
Professor
MA 124 - Spring ’10 - Exam 2 - Prof. Meuser
1) (13 points) Consider the definite integral
Z0
2
1
x+ 2 dx
a) Is this integral improper or not ? Explain your answer.
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
converge find the limit. Explain your answers using properties of limits.
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
QUESTION 7 IS ON THE BACK OF THIS PAGE
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