Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the domain of the function  ?
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2.
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What is the domain of the function  ?
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3.
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Write the following expression as a logarithm of a single quantity. 
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4.
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Write the following expression as a logarithm of a single quantity. 
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5.
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Find the following limit if it exists:  . Use 
when appropriate.
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6.
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Find the following limit if it exists:  . Use 
when appropriate.
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7.
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Find an equation of the tangent line to the graph of  at the point (1,0).
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8.
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Differentiate the function  .
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9.
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Differentiate 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 the derivative of the function  .
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14.
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Find the slope-intercept equation of the line tangent to the graph of  when  .
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15.
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Use implicit differentiation to find  . 
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16.
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Use implicit differentiation to find  . 
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17.
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Use implicit differentiation to find  at the point  . 
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18.
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Determine the x-coordinate(s) of any relative extrema and inflection
points of the function  .
a. | relative minimum: ; inflection point: | b. | no relative extrema; inflection point:  | c. | relative minimum:
 ; no inflection points | d. | no relative extrema;
inflection point:  | e. | relative maximum:
 inflection point:  |
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19.
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Use logarithmic differentiation to find the derivative of  .
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20.
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Suppose the term of a mortgage t (in years) can be approximated by  where x is the monthly payment in dollars. Use the model to approximate the term
of a home mortgage for which the monthly payment is $  . What is the total amount
paid? Round your answer to the nearest cent. Your answer may be slightly different depending on the
number of digits your technology uses in computations.
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21.
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The relationship between the number of decibels  and the
intensity I of sound in watts per centimeter squared is  .
Determine the number of decibels of a sound with an intensity of  watts per
square centimeter. a. | 250 decibels | b. | 65 decibels | c. | 70
decibels | d. |  decibels | e. | 75
decibels |
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22.
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Suppose the table below shows the temperature  at
which a given liquid boils at selected pressures p (pounds per square inch). A model that
approximates the data is  . Find the rate of change of T with
respect to p when P = 20. Round your answer to two decimal places. P | 5 | 10 | 14.696
(1 atm) | 20 | 30 | 40 | 60 | 80 |
100 | T | 234.68 | 288.88 | 320.55 | 346.89 | 383.19 | 410.28 | 450.7 | 481.26 | 506.22 | | | | | | | | | | |
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23.
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Suppose the table below shows the temperature  at which a given liquid boils at selected pressures
p (pounds per square inch). A model that approximates the data is
 . Find  . | P | 5 | 10 | 14.696
(1
atm) | 20 | 30 | 40 | 60 | 80 | 100 |
T | 204.16 | 236.64 |
256.08 | 272.55 |
295.68 |
313.29 |
340.12 |
360.86 |
378.07 | | | | | | | | | | |
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