MATH 116 — EXAM II
Department of Mathematics
University of Michigan
March 18, 2003
NAME:
ID NUMBER:
SIGNATURE:
INSTRUCTOR:
SECTION NO:
1. This exam has nine pages including this cover. There are nine questions.
2. Use of books, notes, or scratch paper is
NOT
allowed. You may certainly use your calculator
(but not its manual). One 3x5inch notecard is allowed.
3.
Show all of your work!
Partial credit is available for many problems but can only be given
if the graders understand your work. Be sure to explain your reasoning carefully. If you are
basing your reasoning on a graph, then sketch the graph. Include units in your answers whenever
appropriate.
4. One of the skills being tested in this exam is your ability to interpret detailed, precisely worded
directions. Be sure to read the directions carefully and do all that is asked.
5. Stay calm.
PROBLEM
POINTS
SCORE
1
6
2
8
3
12
4
10
5
18
6
10
7
16
8
10
9
10
TOTAL
100
1
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1.
(2 pts each) Circle true or false. No explanation necessary.
True
or
False
: The Taylor series centered at
x
= 2 of
e
x
is
1 + (
x

2) +
(
x

2)
2
2!
+
(
x

2)
3
3!
+
(
x

2)
4
4!
+
(
x

2)
5
5!
+
. . .
True
or
False
: If lim
n
→∞
a
n
= 0, then
∑
∞
n
=0
a
n
converges.
True
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 Winter '08
 Conger
 Math, Derivative, Power Series, Taylor Series, probability density function

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