# 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!

-25-