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MATH 152 Honors
FINAL EXAM
Spring 2012
Sections 201-202
1.
Compute
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16
/12
17
/12
18
/12
19
/12
Total
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P. Yasskin
Multiple Choice: (15 problems, 4 points each)
e
1-15
9x 2 ln x dx
1
2.
a.
2e 3
1
b.
2e
3
2
c.
2e 3
d.
3e 3
3e 2
e.
3e 3
3e 2
Compute
2
1
a.
b.
c.
d.
e.
3.
3
x
1
2
4/3
dx
3
1
3
Find the arclength of the parametric curve
a.
b.
c.
d.
e.
x
t4
y
1 t6
2
for 0
t
1.
61
54
16
9
11
9
1
9
1
54
1
4.
5.
A 2 meter bar has linear density
Find the average density of the bar.
a.
2 kg/m
b.
3 kg/m
c.
4. 5 kg/m
d.
5 kg/m
e.
6 kg/m
A 2 meter bar has linear density
Find the center of mass of the bar.
a.
b.
c.
d.
e.
6.
1
1
x 3 kg/m where x is measured from one end.
5 m
7
5 m
6
6 m
5
7 m
5
42 m
5
If y x satisfies the differential equation
condition y 0
3, find y 4 .
a.
b.
c.
d.
e.
x 3 kg/m where x is measured from one end.
dy
dx
x
y
and the initial
1
2
3
4
5
2
7.
Find an integrating factor for the differential equation
a.
b.
c.
d.
e.
8.
2xy
sin x.
e cos x
e sin x
e cos x
2
ex
2
e x
A sequence is defined recursively by:
a.
b.
c.
d.
e.
dy
dx
a1
4 and a n
1
10a n
16 . Find nlim a n .
2
4
6
8
Diverges
3n
9.
n 2
2 2n
1
a.
2
b.
9
14
9
2
4
Diverges
c.
d.
e.
3
10. Find the radius of convergence of the series
n 1
a.
b.
c.
d.
e.
x 0
b.
c.
d.
2
x
3 n.
0
1
3
1
2
2
3
11. lim sin x
a.
2n
n 1
x cos x
x3
1
6
1
3
1
2
2
3
e.
12. Suppose the series
ne
n2
9
is approximated by its 9 th partial sum
n 1
ne
n2
.
n 1
Use an integral to bound the error in this approximation.
a.
b.
c.
d.
e.
1e
2
1e
2
1e
2
1e
2
1e
2
64
81
100
121
144
4
13. Find the angle between the vectors u
a.
b.
c.
d.
e.
1, 1, 1
and v
1, 2, 1 .
0°
30°
45°
60°
90°
14. If u points South-West and v points Up, which way does u
a.
South-East
b.
North-East
c.
North-West
d.
45° Up from North-West
e.
45° Down from North-West
15. Find a unit vector perpendicular to both a
a.
2, 4, 2
b.
2, 4, 2
c.
3, 2, 1
and b
v point?
1, 0, 1 .
1, 2, 1
d.
1 , 2 , 1
6
6
6
e.
1 ,
6
2 , 1
6
6
5
Work Out (4 questions, 12 points each)
Show all you work.
16. Compute
4
2
x
3
8
x2
dx
4
x 2 is rotated about the y-axis to form a bowl. If the bowl contains 8 cm 3 of
water, what is the height of the water in the bowl?
17. The curve y
6
18. A leaking sandbag is lifted 20 ft at 2 ft/sec. The sandbag starts out weighing 50 lb but is leaking
sand at 3 lb/sec. How much work is done to lift the sandbag?
HINT: What is the weight of the bag when it is y ft above the ground?
19. Determine if the series
n 0
diverges.
If it converges, find the sum.
Circle One:
1 n2n
n!
converges absolutely, converges but not absolutely or
If it diverges, does it diverge to
Converges Absolutely
Fill in the Blank:
Or Circle One:
,
or neither?
Converges Conditionally
Diverges
Converges to
Diverges to
Neither
7