Deck 9: Section 9: Infinite Series

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سؤال
Use the series <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 <div style=padding-top: 35px> for <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 <div style=padding-top: 35px> to approximate the value of <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 <div style=padding-top: 35px> using <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 <div style=padding-top: 35px> . 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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سؤال
Find the sum of the convergent series <strong>Find the sum of the convergent series   by using a well-known function. Round your answer to four decimal places.</strong> A) 0.1671 B) 0.7802 C) 2.4061 D) 0.0870 E) 2.3979 <div style=padding-top: 35px> 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
سؤال
Explain how to use the geometric series <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px> to find the series for the function <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px> .

A) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px>
B) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px>
C) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px>
D) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px>
E) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   <div style=padding-top: 35px>
سؤال
Use the power series <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> to determine a power series centered at 0 for the function <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . .

A) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
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. <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>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.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a geometric power series for the function <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use the power series <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> to determine a power series centered at 0 for the function <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a geometric power series for the function <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 0.

A) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Explain how to use the geometric series <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px> to find the series for the function <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px> .

A) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px>
B) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px> and multiply the series by <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px>
C) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px> and divide the series by 9
D) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px> and divide the series by 9
E) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   <div style=padding-top: 35px>
سؤال
Find the sum of the convergent series <strong>Find the sum of the convergent series   by using a well-known function. Round your answer to four decimal places.</strong> A) 0.1419 B) 0.2450 C) 0.8961 D) 0.1651 E) 0.1974 <div style=padding-top: 35px> 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
سؤال
Find a power series for the function <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> centered at 1.

A) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use the power series <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> to determine a power series for the function <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 9: Section 9: Infinite Series
1
Use the series <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 for <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 to approximate the value of <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 using <strong>Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.</strong> A) 0.125 B) 0.111 C) 0.143 D) 0.100 E) 0.133 . Round your answer to three decimal places.

A) 0.125
B) 0.111
C) 0.143
D) 0.100
E) 0.133
0.125
2
Find the sum of the convergent series <strong>Find the sum of the convergent series   by using a well-known function. Round your answer to four decimal places.</strong> A) 0.1671 B) 0.7802 C) 2.4061 D) 0.0870 E) 2.3979 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
0.0870
3
Explain how to use the geometric series <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   to find the series for the function <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with   .

A) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with
B) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with
C) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with
D) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with
E) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> A) replace x with   B) replace x with   C) replace x with   D) replace x with   E) replace x with
replace x with replace x with
4
Use the power series <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   to determine a power series centered at 0 for the function <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)   . .

A) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)
B) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)
C) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)
D) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)
E) <strong>Use the power series   to determine a power series centered at 0 for the function   . .</strong> A)   B)   C)   D)   E)
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Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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6
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. <strong>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.  </strong> A)   B)   C)   D)   E)

A) <strong>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.  </strong> A)   B)   C)   D)   E)
B) <strong>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.  </strong> A)   B)   C)   D)   E)
C) <strong>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.  </strong> A)   B)   C)   D)   E)
D) <strong>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.  </strong> A)   B)   C)   D)   E)
E) <strong>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.  </strong> A)   B)   C)   D)   E)
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7
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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8
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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9
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
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10
Find a power series for the function <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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11
Find a geometric power series for the function <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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12
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
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13
Identify the interval of convergence of a power series <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
B) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
C) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
D) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
E) <strong>Identify the interval of convergence of a power series   .</strong> A)   B)   C)   D)   E)
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14
Use the power series <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   to determine a power series centered at 0 for the function <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)
B) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)
C) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)
D) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)
E) <strong>Use the power series   to determine a power series centered at 0 for the function   .</strong> A)   B)   C)   D)   E)
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15
Find a geometric power series for the function <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)   centered at 0.

A) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
B) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
C) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
D) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
E) <strong>Find a geometric power series for the function   centered at 0.</strong> A)   B)   C)   D)   E)
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16
Explain how to use the geometric series <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   to find the series for the function <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   .

A) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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
B) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   and multiply the series by <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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
C) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   and divide the series by 9
D) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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   and divide the series by 9
E) replace x with <strong>Explain how to use the geometric series   to find the series for the function   .</strong> 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
Find the sum of the convergent series <strong>Find the sum of the convergent series   by using a well-known function. Round your answer to four decimal places.</strong> A) 0.1419 B) 0.2450 C) 0.8961 D) 0.1651 E) 0.1974 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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18
Find a power series for the function <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)   centered at 1.

A) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)
B) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)
C) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)
D) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)
E) <strong>Find a power series for the function   centered at 1.</strong> A)   B)   C)   D)   E)
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19
Use the power series <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   to determine a power series for the function <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)
B) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)
C) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)
D) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)
E) <strong>Use the power series   to determine a power series for the function   .</strong> A)   B)   C)   D)   E)
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