Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Assume that x and y are both differentiable functions of t
. Find  for the equation  .
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2.
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Assume that x and y are both differentiable functions of t.
Find  for the equation  .
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3.
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A point is moving along the graph of the function  such that
 centimeters per second. Find 
when x =  .
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4.
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5.
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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 |
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6.
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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.
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7.
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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?
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8.
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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?
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9.
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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.
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10.
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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 |
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11.
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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.
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12.
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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 |
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13.
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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 |
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14.
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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 |
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15.
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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 |
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16.
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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.
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