Larson_Calculus_10e ch02sec06
MULTIPLE CHOICE
1. Assume that x and y are both differentiable functions of t . Find for the
equation .
a.
b.
c.
d.
e.
2. Assume that x and y are both differentiable functions of t. Find for the
equation .
a.
b.
c.
d.
e.
3. A point is moving along the graph of the function such that centimeters per
second. Find when x = .
a.
b.
c.
d.
e.
4. A point is moving along the graph of the function such that = centimeters
per second. Find when .
a.
b.
c.
d.
e.
5. The radius, r, of a circle is decreasing at a rate of centimeters per minute.
Find the rate of change of area, A, when the radius is .
a.
sq cm/min
b.
sq cm/min
c.
sq cm/min
d.
sq cm/min
e.
sq cm/min
6. The radius r of a sphere is increasing at a rate of inches per minute. Find the rate of change of the
volume when r = inches.
a.
b.
c.
d.
e.
7. A spherical balloon is inflated with gas at the rate of cubic centimeters per minute. How fast is
the radius of the balloon increasing at the instant the radius is centimeters?
a.
b.
c.
d.
e.
8. All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume
changing when each edge is centimeters?
a.
b.
c.
d.
e.
9. A conical tank (with vertex down) is feet across the top and feet deep. If water is flowing into
the tank at a rate of cubic feet per minute, find the rate of change of the depth of the water when
the water is feet deep.
a.
b.
c.
d.
e.
10. A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is
pulled away from the wall at a rate of feet per second. How fast is the top of the ladder moving
down the wall when its base is feet from the wall? Round your answer to two decimal places.
a.
ft/sec
b.
ft/sec
c.
ft/sec
d.
ft/sec
e.
ft/sec
11. A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is
pulled away from the wall at a rate of feet per second. Consider the triangle formed by the side of
the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when
the base of the ladder is feet from the wall. Round your answer to two decimal places.
a.
b.
c.
d.
e.
12. A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is
pulled away from the wall at a rate of feet per second. Find the rate at which the angle between the
ladder and the wall of the house is changing when the base of the ladder is feet from the wall.
Round your answer to three decimal places.
a.
rad/sec
b.
rad/sec
c.
rad/sec
d.
rad/sec
e.
rad/sec
13. A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the
ground (see figure). When he is feet from the base of the light, at what rate is the tip of his shadow
moving?
a.
ft/sec
b.
ft/sec
c.
ft/sec
d.
ft/sec
e.
ft/sec
14. A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the
ground (see figure). When he is feet from the base of the light, at what rate is the length of his
shadow changing?
a.
ft/sec
b.
ft/sec
c.
ft/sec
d.
ft/sec
e.
ft/sec
15. A man feet tall walks at a rate of ft per second away from a light that is ft above the ground
(see figure). When he is ft from the base of the light, find the rate.at which the tip of his shadow is
moving.
a.
ft per minute
b.
ft per minute
c.
ft per minute
d.
ft per minute
e.
ft per minute
16. An airplane is flying in still air with an airspeed of miles per hour. If it is climbing at an angle of
, find the rate at which it is gaining altitude. Round your answer to four decimal places.
a.
b.
c.
d.
e.