Math 116 — Final Exam
December 15, 2011
Name:
Instructor:
Section:
1.
Do not open this exam until you are told to do so.
2. This exam has 12 pages including this cover. There are 10 problems. Note that the problems are not
of equal difﬁculty, so you may want to skip over and return to a problem on which you are stuck.
3. Do not separate the pages of this exam. If they do become separated, write your name on every page
and point this out to your instructor when you hand in the exam.
4. Please read the instructions for each individual problem carefully. One of the skills being tested on
this exam is your ability to interpret mathematical questions, so instructors will not answer questions
about exam problems during the exam.
5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that
graders can see not only your answer but how you obtained it. Include units in your answer where
that is appropriate.
6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad).
However, you must show work for any calculation which we have learned how to do in this course.
You are also allowed two sides of a
3
00
×
5
00
note card.
7. If you use graphs or tables to ﬁnd an answer, be sure to include an explanation and sketch of the
graph, and to write out the entries of the table that you use.
8.
Turn off all cell phones and pagers
, and remove all headphones.
Problem
Points
Score
1
10
2
12
3
10
4
9
5
10
6
7
7
12
8
12
9
11
10
7
Total
100
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page 2
You may ﬁnd the following expressions useful. And you may not. But you may use them if they
prove useful.
“Known” Taylor series (all around
x
= 0
):
sin(
x
) =
x

x
3
3!
+
···
+
(

1)
n
x
2
n
+1
(2
n
+ 1)!
+
······
for all values of
x
cos(
x
) = 1

x
2
2!
+
···
+
(

1)
n
x
2
n
(2
n
)!
+
···
for all values of
x
e
x
= 1 +
x
+
x
2
2!
+
···
+
x
n
n
!
+
···
for all values of
x
ln(1 +
x
) =
x

x
2
2
+
x
3
3

x
4
4
+
···
+
(

1)
n
+1
x
n
n
+
···
for

1
< x <
1
(1 +
x
)
p
= 1 +
px
+
p
(
p

1)
2!
x
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 Fall '07
 Irena
 Math, Calculus, Taylor Series

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