Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find a geometric power series for the function  centered at
0.
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2.
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Find a geometric power series for the function  centered at
0.
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3.
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Find a geometric power series for the function centered at 0, (i) by the
technique shown in Examples 1 and 2 and (ii) by long division.
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4.
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Find a power series for the function  centered at 1.
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5.
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Find a power series for the function  centered at 0.
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6.
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Find a power series for the function  centered at 0.
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7.
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Find a power series for the function  centered at 0.
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8.
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Find a power series for the function  centered at 0.
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9.
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Use the power series  to determine a power series
centered at 0 for the function  .
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10.
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Identify the interval of convergence of a power series  .
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11.
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Use the power series  to determine a power series
centered at 0 for the function  . .
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12.
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Identify the interval of convergence of a power series  .
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13.
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Use the series  for  to
approximate the value of  using  . Round your
answer to three decimal places. a. | 0.125 | b. | 0.111 | c. | 0.143 | d. | 0.100 | e. | 0.133 |
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14.
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Use the power series  to determine a power series
for the function  .
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15.
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Identify the interval of convergence of a power series  .
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16.
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Explain how to use the geometric series  to find the
series for the function  . a. | replace x with  | b. | replace x
with  and multiply the series by  | c. | replace x with  and divide the series by
9 | d. | replace x with  and divide the series by
9 | e. | replace x with  |
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17.
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Find the sum of the convergent series  by using a
well-known function. Round your answer to four decimal places. a. | 0.1671 | b. | 0.7802 | c. | 2.4061 | d. | 0.0870 | e. | 2.3979 |
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18.
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Find the sum of the convergent series  by using a
well-known function. Round your answer to four decimal places. a. | 0.1419 | b. | 0.2450 | c. | 0.8961 | d. | 0.1651 | e. | 0.1974 |
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