Math 202
Final Exam
Spring,2008
Part I
Do all parts of the following six problems.
(1) Compute the derivative
dy
dx
for each of the following (18 points) :
(a)
y
= 2
arctan(3
x
)
;
(b)
y
=
x
2
+
x
x
;
(c)
y
= ln(
q
x
4
+ 3
x
)
.
(2) Compute each of the following integrals(24 points):
(a)
Z
x
3
p
4 +
x
2
dx
;
(b)
Z
x
3

1
x
3
+
x
dx
(c)
Z
cos
3
(
x
)
dx
;
(d)
Z
1
0
x
ln(
x
+ 1)
dx.
(3) Compute each of the following limits (10 points):
(a)
Lim
x
→∞
x
2
+
e
x
x
3
+
e
x
;
(b)
Lim
x
→∞
x
1
/x
.
(4) The region
R
in ﬁrst quadrant of the
xy
plane is bounded by the curves
y
= 9

x
2
,
y
= 0 and
x
= 0. Set up two integrals (method of washers
and method of shells) for the volume of the solid obtained by rotating
R
around the line
x
= 10. Do not compute the value of the integrals(10
points)
(5) Sketch the curve given by the equation
r
= 2+cos(
θ
) in polar coordinates,
labeling the
x
and
y
intercepts, and compute the area it encloses. (8
points)
1
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 Spring '11
 Ocken
 Derivative

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