# Find a power series representation of the following function and determine the radius of convergence

Transcribed Image Text: R-Vs (C) E(-1ye2
Find a power series representation of the following function and determine the radius of convergence.
R-Vs (F) E (-1y-12
f(x)
8-
(A) E (-1yr
-2
R= V2 (B) E (-1y
n=0
(D) E(-1y+1 r-2
8″
R= V2 (E) E
R=V5
(G) E(-1y-1
ga-I R= V2 (H) (-1y 2
R- VE
Evaluate the following integral as a power series.
| In(1 – x) dr
(A) – E
(B) E
(7n + 1X7n)
(C) E
(n+1X6n +6)
(-1y7-5
(D) E
(-1)”,6 -7
(E) E
(n+ 1X7n + 5)
(n-1X6n +7)
(n+1)(6n +6)
(F) – E
(6n + SX6n)
(G) – E
(Н) – У
(n+ IX7A – 5)
(n-1Xón +7)
Find the Taylor series for f(x) =! centered at a = 2.
(-1)” (n+ 1)
(-1y”
(A) E
(x-2y” (B) E (r- 2y (C) E
(-1y -1
(x- 2y (D) E (x – 2y”
(-1y
(E) EIY- (n + 1)
(-1y (n +1)
(-1y-1
2-1 (x-2y
(x- 2)” (F)
(x-2y (G)
(-1y” (n + 1)
(H) E
Find a simplified expression for ().
1/3
(-1y-12.5. . … (3n – 4)
(A)
(-1y-1 3.6.9. .. (3n – 3)
(В)
(-1y” 4·7. 10 * (3n – 2)
3″ n!
3-1 n!
3″ n!
(-1)” 3. 6.9. .. (3n- 3)
(D)
(-1)”-2.5.8.
(E)
(-1)” 2 · 5 •8 . ..
(F)
(3n -2)
3″ n!
3″ n!
3″- n!
(-1y-14.7.10 . …. (3n – 2)
(G)
(-1)” 4-7. 10 …. (3n – 4)
(H)
3-1 n!
3″ n!

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