1. [-/4 Points] DETAILS LARCALC119.9.004.
Find a geometric power series for the function, centered at 0, by the following methods.
1
f(x) =
5+x
(a) by the technique shown in Examples 1 and 2
f(x) =
(b) by long division (Give the first three terms.)
f(x) =
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л-0
2. [-/4 Points] DETAILS LARCALC11 9.9.006.
Find a geometric power series for the function, centered at 0, by the following methods.
6
f(x)=
9-x
f(x) =
(a) by the technique shown in Examples 1 and 2
Σ
(b) by long division (Give the first three terms.)
f(x) =
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3. [-/4 Points]
f(x) = Σ
Л-0
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DETAILS LARCALC11 9.9.007.
Find a power series for the function, centered at c.
f(x)=
c=2
Determine the interval of convergence. (Enter your answer using interval notation.)/n4. [-/4 Points] DETAILS
Find a power series for the function, centered at c.
5
2x
C = 4
f(x) =
f(x) =
n=0
Determine the interval of convergence. (Enter your answer using interval notation.)
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5. [-/4 Points]
f(x) =
f(x) =
Find a power series for the function, centered at c.
4
3x + 2
n=0
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g(x) =
DETAILS
Determine the interval of convergence. (Enter your answer using interval notation.)
-Σ
LARCALC119.9.012.
c=5
6. [-/4 Points] DETAILS
n=0
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LARCALC11 9.9.014.MI.
Find a power series for the function, centered at c.
g(x) =
4x
x²+2x-3
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LARCALC11 9.9.015.
c=0/n7. [-/4 Points]
Find a power series for the function, centered at c.
9
f(x) = Σ
n=0
Determine the interval of convergence. (Enter your answer using interval notation.)
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8. [-/4 Points]
f(x) =
DETAILS LARCALC11 9.9.018.
h(x) =
Use the power series
-
h(x) =
n=0
DETAILS LARCALC11 9.9.019.
to find a power series for the function, centered at 0.
-2
1
2²1
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c=0
Σ(-1), x < 1
n=0
=
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+
Determine the interval of convergence. (Enter your answer using interval notation.)
1
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Use the power series
f(x) =
n=0
to determine a power series for the function, centered at 0,
п-D
DETAILS
f(x)=
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10. [-/4 Points]
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f(x) =
14
(x + 1)
Determine the interval of convergence. (Enter your answer using interval notation.)
Use the power series
n=0
(-1)"x", |x| < 1
DETAILS
f(x) = In(x + 1) =
LARCALC11 9.9.022.
=
Σ(-1) ²² x < 1
n=0
to find a power series for the function, centered at 0.
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7
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LARCALC11 9.9.023.
-dx
x + 1
Determine the interval of convergence. (Enter your answer using interval notation.)
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Use the power series
f(x) =
(-1)^² x < 1
л-0
to find a power series for the function, centered at 0.
f(x) = In(x + 1)
Σ
Determine the interval of convergence. (Enter your answer using interval notation.)
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DETAILS
12. [-/4 Points]
f(x) =
Use the power series
Σ
n=0
LARCALC11 9.9.026.
DETAILS LARCALC11 9.9.028.MI.
n=0
to find a power series for the function, centered at 0.
f(x) = arctan 9x
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Σ(-1)^² x < 1
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Determine the interval of convergence. (Enter your answer using interval notation.)
Master It/n13. [-/4 Points]
Use the power series
f(x) =
Σει
to find a power series for the function, centered at 0.
1
f(x) =
(1-x)²
n=1
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Determine the interval of convergence. (Enter your answer using interval notation.)
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14. [-/4 Points]
DETAILS
Use the fact that
(a)
(b)
-
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DETAILS
LARCALC11 9.9.037.
(1-x)"
#Σ (7)" -E
n=1
÷ [-(9)*-[
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Σ nxn-1 to find the sum of each series.
LARCALC11 9.9.042./n15. [-/4 Points]
LARCALC11 9.9.047.
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)
(−1)″ + 1_
4"n
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16. [-/4 Points]
LARCALC11 9.9.049.
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)
2n
(-1)+1;
5"n
n=0
DETAILS
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DETAILS
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17. [-/4 Points]
LARCALC11 9.9.051.
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)
1
(-1) 62n+1(2n +1)
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DETAILS
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Watch It/n18. [-/4 Points]
DETAILS LARCALC11 9.9.052.
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)
(−1)″ +1-
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19. [-/4 Points]
f(x) = Σ
n=0
Find a power series for the function, centered at c.
5
f(x) =
c=-3
5-x
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1
g2n-1(2n-1)
Determine the interval of convergence. (Enter your answer using interval notation.)
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DETAILS LARCALC11 9.9.501.XP.
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n-06
20. [-/4 Points] DETAILS LARCALC11 9.9.504.XP.
Find the sum of the series. (Round your answer to six decimal places.)
(-1)^2+1
2n +
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