1. Find power series representations for the following functions. State the radius of convergence. (You do NOT need to find the interval of convergence.) Make sure to write your answer in the proper form: (z-a)*, where a is the center. k=0 (a) f(x) = re centered at a = <=0 24+1 EI f(() = 2 + (x)² k=6 ROC=0 laflo Test k+1(k) | | kfl So 20C = 80 e = 2. 2 ex= T = 11 kok! R=0 k! X 26+1 kio ki 2k+1 CD (x²³² 4-0 (b) re lion Iim X O da centered at a = 0 (Use your answer to part (a)!) 4821 Kai S
1. Find power series representations for the following functions. State the radius of convergence. (You do NOT need to find the interval of convergence.) Make sure to write your answer in the proper form: (z-a)*, where a is the center. k=0 (a) f(x) = re centered at a = <=0 24+1 EI f(() = 2 + (x)² k=6 ROC=0 laflo Test k+1(k) | | kfl So 20C = 80 e = 2. 2 ex= T = 11 kok! R=0 k! X 26+1 kio ki 2k+1 CD (x²³² 4-0 (b) re lion Iim X O da centered at a = 0 (Use your answer to part (a)!) 4821 Kai S
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How would I find this power series and use it to solve for part b?
Transcribed Image Text:Show all your work. In particular, you should clearly communicate youur solution by providing arguments and
statements that are complete, logically ordered, and use proper terminology and notation.
1. Find power series representations for the following functions. State the radius of convergence. (You do NOT
need to find the interval of convergence.) Make sure to write your answer in the proper form: C (x- a)*,
where a is the center.
(a) f(x) = re
centered at a =0
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o k!
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ko k!
ROC 0
ルニロ
lasio Test
liem
こ
kio ks.
とA(
zkrl
lim
ニ
So 2OC =
(b) / ze
Flx)= į ! (x)
da centered at a = 0 (Use your answer to part (a)!)
Lい
ko k!.
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1
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