Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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2.
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If the surface area of a sphere is shrinking at the
rate of 0.1 sq cm/h when the radius is  cm,
the rate of change of the radius is
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3.
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If the radius of a circle is increasing at a certain rate, the circumference of
the circle is increasing at
a. | the same rate | b. | the rate times  | c. | the rate times  | d. | the rate times  |
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4.
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A small rocket rising vertically is tracked by an observer located 25 km from
the lift-off point. At a certain moment, the angle between the observer’s line of sight and the
horizontal is  , and it is changing at rate of 0.25 radian per
minute. How fast is the rocket rising at this moment? a. | 3.6084 km/min | b. | 4.1667 km/min | c. | 4.6875
km/min | d. | 8.3333 km/min |
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5.
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Let  . The set of all critical numbers of  is
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6.
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Let  . The set of all critical numbers of  is
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7.
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Let  on  . The absolute minimum and
maximum of  are located respectively at 
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8.
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The function  represents the concentration of a medication (in
 ) in a patient’s bloodstream after t hours. What is the maximum concentration
in the time interval  ?
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9.
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Let  . Then  has a relative maximum at 
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10.
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Let  . Then  has a point of inflection at
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11.
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 At which of the four points on the graph in
the figure above is  negative and  positive?
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12.
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Determine which of the following is true for the limit  .
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13.
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 is
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14.
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Determine which of the following is not true for the graph of  .
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15.
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Determine which of the following is not true for the graph of  .
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16.
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Determine which of the following is not true for the graph of  .
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17.
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The maximum area of a rectangular piece of land that can be enclosed by 100
yards of fencing is
a. |  square yards | b. | 
square yards | c. |  square yards | d. | 
square yards |
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18.
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If  and  , the maximum value of  is
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19.
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Suppose that, when a stone is thrown upwards with a speed of 60 miles an hour,
its height,  feet, after  seconds, is
given by  . The maximum height of the stone is
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20.
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 A rancher has 7200 feet of fencing and she
plans to use it to create three rectangular enclosures, arranged as shown in the figure above. The
width of the larger enclosure is three times the width of the identical smaller enclosures. What is
the largest total area she can enclose?
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21.
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The antiderivative of  is
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22.
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The antiderivative of  is
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23.
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The particular solution of the differential equation 
satisfying the boundary condition when is  is
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24.
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The particular solution of the differential equation  satisfying the
initial conditions  and  is
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25.
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The particular solution of the differential equation  satisfying the
boundary conditions when is  and  is
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