Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Solve the following equation for  . 
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2.
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Solve the following equation for  . 
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3.
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Solve the following equation for  . 
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4.
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Solve the following equation for  . 
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5.
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Find an equation of the tangent line to the graph of  at the point
 .
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6.
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Differentiate the function   .
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7.
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Find  if  .
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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  if  .
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10.
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Differentiate the function  .
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11.
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Find the derivative of the function  . Simplify your
answer.
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12.
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Find the derivative of the function  . Simplify your
answer.
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13.
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Find  if 
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14.
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Use implicit differentiation to find  
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15.
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Find  if  .
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16.
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Find all points of inflection on the graph of the function  .
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17.
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The value V (in dollars) of an item t years after it is purchased
is  . Find the rate of change of V with
respect to t when  . Round your answer to two decimal
places. a. | –3,115.72 dollars/year | b. | –1,944.61
dollars/year | c. | 3,115.72 dollars/year | d. | –1,836.5 dollars/year | e. | 1,944.61
dollars/year |
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18.
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A meteorologist measures the atmospheric pressure P (in kilograms per
square meter) at altitude h (in kilometers). The data are shown below. Use the regression
capabilities of the graphing utility to find a linear model for the revised data points obtained by
plotting the points  
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19.
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A meteorologist measures the atmospheric pressure P (in kilograms per
square meter) at altitude h (in kilometers). The data are shown below. Find the rate of change
of the pressure with respect to altitude when  using the relation
 . Round your answer to one decimal
place. 
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20.
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The table lists the approximate value V of a mid-sized sedan for the
years 2003 through 2009. The variable t represents the time in years, with  corresponding to 2003. Use the regression capabilities of a graphing utility to fit an
exponential model to the data. Round all numerical values in your answer to four decimal places. Your
answer may be slightly different depending on the number of digits your graphing utility uses in
computations. 
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21.
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The table lists the approximate value V of a mid-sized sedan for the
years 2003 through 2009. The variable t represents the time in years, with 
corresponding to 2003. Find the rate of change in the value of the sedan when 
using the exponential model  . Round your answer to two decimal
places. 
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22.
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Find the indefinite integral. 
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23.
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Find the indefinite integral. 
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24.
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Evaluate the definite integral. 
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25.
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Evaluate the definite integral. 
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26.
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Find the indefinite integral 
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27.
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A valve on a storage tank is opened for 3 hours to release a chemical in a
manufacturing process. The flow rate R (in liters per hour) at time t (in hours) is
given by the exponential model  Use the definite integral to approximate the
number of liters of chemical released during the first 3 hours. Round your answer to two decimal
places. a. | 1,594.86 liters | b. | 1,222.68 liters | c. | 1,887.64
liters | d. | 1,732.19 liters | e. | 1,340.70 liters |
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