1. [-/4 Points]
State where the power series is centered.
(-1)^(4n-1) n
4ºn!
n=1
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2. [-/4 Points]
n=0
DETAILS LARCALC11 9.8.006.
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State where the power series is centered.
(-1)²(x - 577) 9
(9n)!
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LARCALC11 9.8.008.
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Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or -INFINITY, respectively.)
Σ(-1)7 n+3
n = 0
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n=0
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4. [-/4 Points] DETAILS
Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or -INFINITY, respectively.)
(-1)" xn
2
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(4n)!
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LARCALC11 9.8.009.
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5. [-/4 Points] DETAILS
Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or -INFINITY, respectively.)
LARCALC11 9.8.012.MI.
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LARCALC11 9.8.013.
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is
(-1)"+¹(n + 2)x"
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7. [-/4 Points] DETAILS LARCALC11 9.8.020.MI.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is
(5x)
)
- (2n)!
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8. [-/4 Points] DETAILS
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter you
Σ (2n)!()*
n=0
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9. [-/4 Points] DETAILS
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LARCALC11 9.8.021.
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LARCALC11 9.8.024.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
1st worksheet (20 questions) II do all/n9. [-/4 Points] DETAILS LARCALC11 9.8.024.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
(-1)^n!(x-9)"
7"
n=0
Ox = 0
07 < x≤9
Ox # 9/7
+
Ox + 9
Ox = 9
07 ≤ x < 9
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n=1
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10. [-/4 Points] DETAILS
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
(-1)"+¹(x-2)^
n6
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LARCALC11 9.8.025.
11. [-/4 Points]
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
(x-3)" +1
(n+1)9"+1
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LARCALC11 9.8.026.
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Cancel/n12. [-/4 Points] DETAILS LARCALC11 9.8.028.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is
(-1)+¹(x-9)
ng
n=1
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13. [-/4 Points] DETAILS LARCALC11 9.8.030.
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is
Σ (-1)" x8n +7
0-0
8n +7
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14. [-/4 Points]
n=1
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is
n!(x + 9)"
1.3.5... (2n-1)
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n=0
LARCALC11 9.8.038.
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15. [-/4 Points] DETAILS LARCALC11 9.8.040.
Find the radius of convergence of the power series, where k is a positive integer.
(n!)*x^
(kn)!/n16. [-/4 Points] DETAILS LARCALC11 9.8.042.
Find the interval of convergence of the power series, where c> 0. (Be sure to include a check for convergence at the endpoints of the interval. Enter your answer using interval notation.)
(-1)"+¹(x-c)"
nen
n=1
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Σ
n=1
17. [-/4 Points] DETAILS LARCALC11 9.8.046.
Write an equivalent series with the index of summation beginning at n = 1.
(-1)" + 1(n+1)x"
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18. [-/4 Points] DETAILS LARCALC11 9.8.050.
Find the intervals of convergence of f(x), f'(x), f'(x), and [f(x) dx. (Be sure to include a check for convergence at the endpoints of the intervals. Enter your answer using interval notation.)
f(x) = Σ (-1)"+¹(x-4)"
n=1
n4"
(a) f(x)
(b) f'(x)
(c) F"(x)
(d)
f(x) dx/n19. [-/4 Points] DETAILS LARCALC11 9.8.052.
Find the intervals of convergence of f(x), f'(x), f"(x), and
f(x) =
(a) f(x)
(b) f'(x)
(c) F"(x)
(d) [1(x) d
dx
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(-1)"+¹(x-4)"
n
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20. [-/4 Points]
Let g(x) = 1 + 8x + x² + 8x³ + x²+, where the coefficients are C2n = 1 and C2n + 1 = 8 for n ≥ 0.
(a) Find the interval of convergence of the series. (Enter your answer using interval notation.)
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(b) Find an explicit formula for g(x).
g(x) =
d ff(x) dx.
) dx. (Enter your answer using interval notation. Be sure to check for convergence at the endpoints of the interval.)
LARCALC11 9.8.078.
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