Math 202
Final Exam
Fall,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
= ln(
1
x
+ 1
)
.
(b)
y
= arcsin(
√
x
);
(c)
y
= sin(
x
)
x
+ sin(
x
);
(2) Compute each of the following integrals(24 points):
(a)
Z
x
3
+ 2
x
3

x
dx
;
(b)
Z
tan(
x
) sec
4
(
x
)
dx
;
(c)
Z
p
4

x
2
dx
;
(d)
Z
1
0
arctan(
x
)
dx.
(3) Compute each of the following limits (10 points):
(a)
Lim
x
→∞
√
x e

x
;
(b)
Lim
x
→
1
+
x
1
/
(
x

1)
.
(4) The region
R
in first quadrant of the
xy
plane is bounded by the curves
y
= sin(
πx
) and
y
= 2
x
.
Set up two integrals (method of washers and
method of shells) for the volume of the solid obtained by rotating
R
around
the line
y
= 2. Do not compute the value of the integrals(10 points)
(5) Sketch the curve given by the equation
r
= 3+sin(
θ
) in polar coordinates,
labeling the
x
and
y
intercepts, and compute the area it encloses.
(8
points)
1
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Part II
Do all parts of three out of the following four problems (10 points
each)
(7) (a) A 16 pound pull extends a spring 6 inches (= one half of a foot).
Compute the work done stretching the spring an additional
foot.
(b) Evaluate the integral or show it is divergent:
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 Spring '11
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