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Calculus II V1102 Section 007,
Fall 2007 Final Exam
Thomas D. Peters
Name:
December 18, 2007
Do all problems, in any order.
Show your work. An answer alone may not receive full credit.
No notes, texts, or calculators may be used on this exam.
Problem
Possible
Points
Points
Earned
1
8
2
13
3
9
4
5
5
4
6
6
7
5
8
5
9
5
10
9
11
6
TOTAL
75
1
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(a)(4 pts) Compute
Z
e
2
x
√
e
2
x
+ 1
dx
(b)(4 pts) Compute
Z
e
x
√
e
2
x
+ 1
dx
2
2.
In this problem we ﬁnd the exact value of
S
=
∞
X
n
=0
(

1)
n
3
n
+ 1
(a)(2 pts) Explain why
S
converges.
(b)(3 pts) Show that
S
=
Z
1
0
dt
1 +
t
3
by expanding the integrand as a series and integrating term by term.
(c)(3 pts) Use partial fractions to decompose
1
t
3
+ 1
(d)(5 pts) Use your answer from (c) to compute
Z
1
0
dt
1 +
t
3
.
3
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True or false. You MUST explain your answer
(a)(3 pts) If
{
a
n
}
and
{
b
n
}
are divergent sequences then
{
a
n
b
n
}
is also a divergent sequence.
(b)(3 pts) If
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This note was uploaded on 10/18/2011 for the course MATH V1102 taught by Professor Mosina during the Fall '08 term at Columbia.
 Fall '08
 Mosina
 Calculus

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