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Stewart_Calc_7ET ch15sec08
MULTIPLE CHOICE
1. Evaluate where and T is the region bounded by the
paraboloid and the plane
a.
b.
c.
d.
2. Use cylindrical coordinates to evaluate where T is the solid bounded by
the cylinder and the planes and
a.
b.
c.
d.
3. Use cylindrical coordinates to evaluate
a.
b.
c.
d.
7
3
1
7
49
3
7
2
14
21
3
12
112
3
2
14
4. Use cylindrical coordinates to evaluate the triple integral
where E is the solid that lies between the cylinders and above the
xy-plane and below the plane .
a.
8.57
b.
0
c.
3.4
d.
9.19
e.
0.54
5. Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate
where E lies above the paraboloid and below the plane .
a.
160.28
b.
175.37
c.
d.
176.38
e.
175.93
6. Use cylindrical coordinates to evaluate
where E is the region that lies inside the cylinder and between the planes
.
Round the answer to two decimal places.
a.
b.
2218.41
c.
2931.90
d.
2818.41
e.
2431.90
NUMERIC RESPONSE
1. The joint density function for random variables and is for
and otherwise. Find the value of the constant
.
Round the answer to the nearest thousandth.
2. Find the region E for which the triple integral is a maximum.
3. Use cylindrical coordinates to find the volume of the solid that the cylinder cuts
out of the sphere of radius 3 centered at the origin.
SHORT ANSWER
1. Find the center of mass of a homogeneous solid bounded by the paraboloid
and
