Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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A sufficient condition for a function
 on  to be integrable
is
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2.
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Which of the following limits is equal to  ?
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3.
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Shown above is a slope
field for which of the following differential equations?
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Short Answer
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4.
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Suppose  is the lower sum of the area enclosed by the graph  the x-axis, and the lines  and  by partitioning  into four subintervals  ,  ,  , and  .
Then 
is
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5.
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 Graph of f
The graph of the piecewise-defined
function f is shown in the figure above. What is  ?
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6.
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7.
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By part 2 of the Fundamental Theorem of Calculus
,  is
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8.
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9.
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If  , then 
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10.
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11.
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The bounds m and M used in the Bounds
on an Integral Theorem for  are
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12.
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The average value of  over 
is
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13.
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The indefinite integral  is
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14.
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The indefinite integral  is
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15.
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The indefinite integral  is
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16.
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The indefinite integral  is
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17.
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If  is an even function  ,and  , then
is
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18.
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19.
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What is the general solution to the differential
equation  ?
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Essay
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20.
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 The function f is defined on the
closed interval  . The graph of f shown in the figure above
consists of three line segments. Let g be the function defined by  for  . (a) Find  . (b) Find values of
x for which g has a local minimum. Justify your answer. (c) What is the
minimum value of  on the interval  ? Justify your
answer. (d) On what open interval(s) contained in  is
the graph of g increasing and concave down? Give a reason for your answer.
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