Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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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2.
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Let  be an integrable
function on  . Which of the following is not
always true?
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3.
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 Graph of f
The graph of the piecewise-defined
function f is shown in the figure above. What is  ?
a. |  | b. |  | c. | 9.3 | d. | 1.5 |
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4.
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5.
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6.
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Which of the following limits is equal to  ?
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7.
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The derivative  is
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8.
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By part 2 of the Fundamental Theorem of Calculus
,  is
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9.
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10.
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The bounds m and M used in the Bounds
on an Integral Theorem for  are
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11.
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The average value of  on  is
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12.
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The indefinite integral  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
a. |  | b. |  | c. | 0 | d. | 1 |
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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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20.
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 Shown above is a slope field for which of
the following differential equations?
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Essay
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21.
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Time (h) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | Rate (l/h) | 785 | 552 | 478 | 465 | 525 | 679 | 815 | | | | | | | | |
The
table above shows the rate (in liters per hour) at which water pours over a spillway, recorded at
two-hour intervals. (a) Estimate the total volume of water that
has drained over  by finding the left and right Riemann sums of the
data and averaging them. (b) The quadratic regression function for the data is  .
Find the indefinite integral of this function. (c) Use  to make a second
estimate of the total volume of water that has drained.
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