Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Evaluate the expression  without using a
calculator.
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2.
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Evaluate the expression  without using a
calculator.
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3.
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Evaluate the expression  without using a
calculator. a. |  | b. |  | c. | 3 | d. | 5 | e. | 4 |
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4.
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Write the following expression in algebraic form. 
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5.
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Write the following expression in algebraic form. 
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6.
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Solve the following equation for  . 
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7.
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Solve the following equation for  . 
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8.
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Find the derivative of the function  .
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9.
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Find the derivative of the function  .
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10.
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Find the derivative of the function  .
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11.
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Find the derivative of the function  .
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12.
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Find the derivative of the function  .
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13.
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Find an equation of the tangent line to the graph of  at the point
 .
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14.
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Find the slope-intercept form of the equation of the line tangent to the graph
of  .
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15.
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An airplane flies at an altitude of 14 miles toward a point directly over an
observer. Consider  and x as shown in the following
figure. Write  as a function of x. 
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16.
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An airplane flies at an altitude of 6 miles towards a point directly over an
observer. Consider  and x as shown in the following
figure. The speed of the plane is 400 miles per hour. Find  when  .
Round your answer to three decimal places.  a. | –17.647 rad/hr | b. | 2.941 rad/hr | c. | 17.647
rad/hr | d. | 0.044 rad/hr | e. | –8.824
rad/hr |
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17.
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In a free-fall experiment, an object is dropped from a height of 256 feet. A
camera on the ground 500 feet from the point of impact records the fall of the object as shown in the
figure. Assuming the object is released at time t = 0. At what time will the object reach the
ground level?  a. | 3 seconds | b. | 6 seconds | c. | 7
seconds | d. | 5 seconds | e. | 4 seconds |
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18.
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In a free-fall experiment, an object is dropped from a height of 144 feet. A
camera on the ground 500 feet from the point of impact records the fall of the object as shown in the
figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of
elevation of the camera when  . Round your answer to four decimal
places.  a. | –0.6006 rad/sec | b. | –0.0581 rad/sec | c. | 0.0601
rad/sec | d. | 0.0581 rad/sec | e. | –0.0601
rad/sec |
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19.
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An 85-foot billboard is perpendicular to a straight road and is 50 feet from the
road as shown in the figure. Find the point on the road such that the angle 
subtended by the billboard is a maximum. How far is this point from the point on the road directly
across from the billboard (in feet)? Round your answer to two decimal places.  a. | 50.00 ft | b. | 29.41 ft | c. | 41.08
ft | d. | 82.16 ft | e. | 85.00 ft |
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20.
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A petrol car is parked 40 feet from a long warehouse (see figure). The revolving
light on top of the car turns at a rate of 30 revolutions per minute. Write 
as a function of x.
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21.
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A petrol car is parked 50 feet from a long warehouse (see figure). The revolving
light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam
moving along the wall when the beam makes an angle of  with the perpendicular from
the light to the wall.
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