Prof. Girardi
Math 142
Spring 2010
04.29.2010
Final Exam
MARK BOX
problem
points
1(23)/2(10)/3(7)
40
4
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
10
13
10
take home
10
150
NAME
(legibly printed):
class PIN:
If you do not make at least a 50% (i.e. at least 20 of the
40 possible points) on problems 1, 2, and 3, then you will
recieve a zero on the remainder of the exam.
You were
warned.
INSTRUCTIONS
:
(1) To receive credit you must:
(a)
work in a logical fashion, show all your work, indicate your reasoning
;
no credit will be given for an answer that
just appears
;
such explanations help with partial credit
(b) if a line/box is provided, then:
— show you work BELOW the line/box
— put your answer on/in the line/box
(c) if no such line/box is provided, then box your answer
(2) The
mark box
indicates the problems along with their points.
Check that your copy of the exam has all of the problems.
(3) You may
not
use a calculator, books, personal notes.
(4) During this exam, do not leave your seat. If you have a question, raise your hand. When
you finish: turn your exam over, put your pencil down, and raise your hand.
(5) This exam covers (from
Calculus
by Stewart, 6
th
ed., ET):
7.1  7.5, 7.8, 11.1  11.8, 6.1  6.3, 10.3, 10.4. .
Problem Inspiration
: See the answer key.
Honor Code Statement
I understand that it is the responsibility of every member of the Carolina community to uphold and maintain
the University of South Carolina’s Honor Code.
As a Carolinian, I certify that I have neither given nor received unauthorized aid on this exam.
Furthermore, I have not only read but will also follow the above Instructions.
Signature :
0
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1.
Fill in the blanks.
•
.
R
du
u
=

u

+
C
•
.
R
cos
u du
=
+
C
•
.
R
sin
u du
=
+
C
•
.
R
tan
u du
=
+
C
•
.
R
cot
u du
=
+
C
•
.
R
sec
u du
=
+
C
•
.
R
csc
u du
=
+
C
•
.
R
sec
2
u du
=
+
C
•
.
R
sec
u
tan
u du
=
+
C
•
.
R
csc
2
u du
=
+
C
•
.
R
csc
u
cot
u du
=
+
C
•
.
If
a
is a contant and
a >
0 then
R
1
a
2
+
u
2
du
=
+
C
•
.
If
a
is a contant and
a >
0 then
R
1
√
a
2

u
2
du
=
+
C
•
.
If
a
is a contant and
a >
0 then
R
1
u
√
u
2

a
2
du
=
+
C
•
.
Partial Fraction Decomposition. If one wants to integrate
f
(
x
)
g
(
x
)
where
f
and
g
are polyonomials
and [degree of
f
]
≥
[degree of
g
], then one must first do
•
.
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 Fall '11
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 Math, Calculus, Mathematical Series, +C

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