Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Let  . Which of the following is true for  ?
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2.
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The largest set on which  is continuous is
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3.
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 is a. | 0 | b. | 1 | c. |  | d. |  |
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4.
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An equation of the tangent line to the graph
 at the point  .
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5.
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Let  . Then  is
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6.
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Let  . Assuming  is
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7.
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Let  . Then  is
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8.
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Let  . Then  is
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9.
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Let  . Then  is
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10.
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11.
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12.
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13.
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Let  . Then  has a relative minimum at 
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14.
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Let  . Then  has a point of inflection at 
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15.
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A rectangular sheet of cardboard is 24 inches by 9 inches. Equal squares are cut
out at the corners and the flaps are turned up to form an open box. The maximum volume of the box, in
cubic inches, is
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16.
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Let  be an integrable function on
 . Which of the following is always true?
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17.
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The derivative  is
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18.
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Which of the following is a formula for  ?
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19.
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20.
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The indefinite integral  is
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21.
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The indefinite integral  is
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22.
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The definite integral  is
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23.
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The differential equation  describes the change in velocity of
a skydiver in freefall in meters per second. If the initial velocity of the skydiver is 0 m/s, which
function models the skydiver’s velocity over time?
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Essay (Extra Credit)
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24.
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 The graph of the piecewise-defined function
f is shown in the figure above. (a) Name all values of
x at which f has a discontinuity and classify them as removable, jump, or infinite
discontinuities. Justify your classifications. (b) How could you remove a discontinuity by
redefining f at a single point? (c) Identify all vertical asymptotes of f.
Justify your answer. (d) If f has a horizontal asymptote at  as
x decreases without bound, what limit must be true?
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