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Exam #1
APPM 1360
Fall 2006
ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture
section (4) your instructor’s name, and (5) a grading table. You must work all of the problems on the exam.
Show ALL of your work in your bluebook and box in your ﬁnal answer. A correct answer with no relevant
work may receive no credit, while an incorrect answer accompanied by some correct work may receive
partial credit. Text books, class notes, and calculators are NOT permitted. A onepage crib sheet is allowed.
1.
(
24 points, 6 each
) Evaluate and simplify your answers as appropriate:
(a)
d
d
x
ln
(
cos
x
)
,
(b)
d
d
x
(
x
x
)
,
(c)
Z
sinh
(
kx
)
d
x
,
k
is constant,
(d)
Z
2 e
2
x
cosh
(
2
x
)
d
x
2.
(
15 points
) Consider the following di
ﬀ
erential equation and initial condition
d
y
d
x
=
e
x
(
y

1
)
2
,
y
(
0
) =
1
2
(a) (
10 points
) Solve the equation with this initial condition.
(b) (
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 Winter '06
 LIM,JISUN

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