Math 116 — First Midterm
February 2011
Name:
EXAM SOLUTIONS
Instructor:
Section:
1.
Do not open this exam until you are told to do so.
2.
This exam has 10 pages including this cover. There are 8 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
17
3
15
4
15
5
8
6
12
7
11
8
12
Total
100
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Math 116 / Exam 1 (February 2011)
page 2
1
. [10 points] Indicate if each of the following statements are true or false by circling the correct
answer.
Justify your answers.
a
. [2 points]
If
F
(
x
) is an antiderivative of an even function
f
(
x
), then
F
(
x
) must also be
an even function.
True
False
Solution:
f
(
x
) = 3
x
2
has
F
(
x
) =
x
3
+ 1 as an antiderivative which is not even (not odd
either).
b
. [2 points]
If
G
(
x
) is an antiderivative of
g
(
x
) and (
G
(
x
)

F
(
x
))
0
= 0, then
F
(
x
) is an
antiderivative of
g
(
x
).
True
False
Solution:
g
(
x
) =
G
0
(
x
) =
F
0
(
x
) hence
F
(
x
) is an antiderivative of
g
(
x
).
c
. [2 points]
Let
f
(
t
) =
bt
+
ct
2
with
b >
0 and
c >
0, then Left(
n
)
≤
R
10
0
f
(
t
)
dt
for all
n
.
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 Math, Calculus

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