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APPM 1360
EXAM #2
FALL 2007
On the front of your bluebook, please write: a grading key, your name, student ID, and
section and instructor (Dougherty, section 10, or Li, section 30 with lecture at 1 pm or
section 20 with lecture at 2 pm).
This exam is worth 100 points and has 5 questions. A list of
formulas is given on the back of this exam.
Show all work!
Answers with no justiﬁcation will receive no
points.
1. (30 points) Evaluate the following integrals. If an integral is improper, determine whether it converges
or diverges. If it converges, evaluate it. If it diverges, justify your answer.
(
a
)
Z
e
1
x
ln(
x
)
dx
(
b
)
Z
1
/
2
0
6
√
1

4
x
2
dx
(
c
)
Z
1

1
1
t
3
dt
2. (20 points) Determine whether the following sequences converge or diverge. If the sequence converges,
ﬁnd its limit.
(
a
)
a
n
= 1 + (

1)
n
(
b
)
b
n
=
1
√
n
2
+
n

√
n
2
+ 1
for
n
≥
2
(
c
)
c
n
=
n
ln
±
1 +
2
n
²
3. (15 points) Consider the sequence
a
n
=
3
n
(
n
+ 1)
and the series
∞
X
n
=1
a
n
.
(a) Does the sequence
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This note was uploaded on 05/01/2008 for the course APPM 1360 taught by Professor Lim,jisun during the Winter '06 term at Colorado.
 Winter '06
 LIM,JISUN

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