Larson_Calculus_10e ch13sec05
MULTIPLE CHOICE
1. Find using the appropriate Chain Rule for where .
a.
116t
b.
58t
c.
104t
d.
32t
e.
174t
2. Let , where and . Find .
a.
b.
c.
d.
e.
3. Let , where , , and . Find .
a.
b.
c.
d.
e.
4. The parametric equations for the paths of two projectiles are given below. At what rate is the distance
between the two objects changing at ? Round your answer to two decimal places.
a.
0.86
b.
1.54
c.
0.58
d.
–1.73
e.
–0.65
5. Find using the appropriate Chain Rule for where and , and evaluate
the partial derivative at and . Round your answer to two decimal places.
a.
–8.83
b.
–5.89
c.
–6.62
d.
2.72
e.
–8.09
6. Find using the appropriate Chain Rule for where and , and evaluate
the partial derivative at and . Round your answer to two decimal places.
a.
1,209.99
b.
806.71
c.
1,210.14
d.
806.69
e.
1,209.20
7. Find using the appropriate Chain Rule for where , and
.
a.
b.
c.
d.
e.
8. Find using the appropriate Chain Rule for where , and
.
a.
b.
c.
d.
e.
9. Differentiate implicitly to find .
a.
b.
c.
d.
e.
10. Differentiate implicitly to find , given .
a.
b.
c.
d.
e.
11. Differentiate implicitly to find , given .
a.
b.
c.
d.
e.
12. The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is
decreasing at a rate of 4 inches per minute. What is the rate of change of the volume when the radius is
14 inches and the height is 32 inches?
a.
b.
c.
d.
e.
13. \The radius of a right circular cylinder is increasing at a rate of 9 inches per minute, and the height is
decreasing at a rate of 7 inches per minute. What is the rate of change of the surface area when the
radius is 12 inches and the height is 32 inches?
a.
b.
c.
d.
e.
14. The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per
minute, and the height is increasing at a rate of 12 centimeters per minute (see figure). Find the rate at
which the volume is changing when the two radii are 15 centimeters and 30 centimeters, and the height
is 10 centimeters.
a.
b.
c.
d.
e.
15. The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per
minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at
which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the
height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round
your answer to two decimal places.
a.
b.
c.
d.
e.