Name
Sec
(Print)
First Last
Signature
MATH 152
FINAL EXAM
Sections 531-533
Version A
Spring 2012
/4
Compute
/60
16
/12
17
/12
18
/12
19
/12
Total
/108
P. Yasskin
Multiple Choice: (15 questions, 4 points each)
1.
1-15
cos sin 3 d
0
a.
b.
c.
d.
e.
2.
1
2
1
4
1
8
1
16
1
32
Compute
ln 2
xe x dx
0
a.
b.
c.
d.
e.
3.
1
1 ln 2
2
2
1
1 ln 2
2
2
1 ln 2 1
2
2
1 ln 2 1
2
2
Divergent
Find the average value of f x
a.
b.
c.
d.
e.
cos x on the interval
4
x
4
.
2 2
2
2
1
2
2
1
4.
The partial fraction decomposition of
a.
b.
c.
d.
e.
5.
1
x
1
x
1
x
1
1
x
x
x
1
is
1
x
1
x
1
1
x
1
1
1
1
x
The base of a solid is the semi-circle between y
9 x 2 and the x-axis.
The cross sections perpendicular to the x-axis are squares. Find the volume of the solid.
b.
9
2
9
c.
9
d.
18
e.
36
a.
6.
1
x
1
x2
The region bounded by x
0,
x
cos y,
y
0,
y
4
Which integral gives the volume of the solid of revolution?
/4
a.
is rotated about the x-axis.
2 cos 2 y dy
0
2 /2
2 x arccos x dx
b.
0
/4
2 y cos y dy
c.
0
2 /2
d.
cos 2 x
x 2 dx
0
/4
e.
2 y 2 dy
0
2
7.
As n approaches infinity, the sequence a n
converges to
b.
d.
converges to 0
converges to 1
2
converges to 1
e.
diverges
8.
n 2
9.
3n
4n 1
b.
9
7
4
c.
9
d.
3
e.
Diverges
a.
cos n
n2
1
2
a.
c.
1
0.1
Estimate
sin x 2 dx to within an error of |E|
0. 0001,
HINT: Use a Maclaurin series.
0
a.
0. 1
b.
0. 1
c.
d.
e.
0. 1
0. 1
6
2
3
0. 1
6
6
0. 1 3
3
0. 1 2
3
10. Compute
lim
x 0
sin 2x 2x
3x 3
1
9
4
8
9
4
3
4
9
a.
b.
c.
d.
e.
n
11. Compute
n 1
1
n
n
1
2
1
2
a.
c.
1
2
1
d.
2
e.
Divergent
b.
n
12. If g x
cos x 2 , what is g
8
0 , the 8 th derivative at zero?
HINT: What is the coefficient of x 8 in the Maclaurin series for cos x 2 ?
a.
b.
c.
d.
e.
1
8 7 6 5
4!
1
4!
8 7 6 5
1
8!
4
13. A vector u has length 5. A vector v has length 4. The angle between them is 60°. Find u v.
d.
10
1
40
3
40
40
e.
10 3
a.
b.
c.
14. If u points North and v points South-East, then u
a.
Up
b.
Down
c.
East-North-East
d.
West-South-West
e.
North-West
15. Find the area of a triangle with edges a
a.
1
b.
2
3, 2, 1
v points
and b
1, 0, 1 .
6
c.
d.
6
e.
2 6
5
Work Out (4 questions, 12 points each)
Show all you work.
16.
12 points
Compute
x2 9
dx.
x
3 2
3
17.
12 points
Find the work done to pump
the water out the top of a hemispherical bowl
of radius 5 cm if it is filled to the top.
The density of water is
1
gm
cm
The acceleration of gravity is g
3
.
980
cm
sec
2
.
6
18.
19.
12 points
Find the arc length of the curve y
x2
4
ln x
2
between x
1 and x
e.
x 3 n
. Be sure to check
4 ln n
n 2
the endpoints. Name or state any test you use and check the conditions.
12 points
Find the radius and interval of convergence of
Radius: R
Interval:
7