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Why did we plug in x = 1/2 at the last part of the solution for the second problem

Why did we plug in x = 1/2 at the last part of the solution for the second problem

Advanced Engineering Mathematics
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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Why did we plug in x = 1/2 at the last part of the solution for the second problem.

x2 Find a power series representation for f(x) 1+ x3* By differentiating the power series obtained in (a), find the exact value of (-1)"(3n + 2) n=0
Transcribed Image Text:x2 Find a power series representation for f(x) 1+ x3* By differentiating the power series obtained in (a), find the exact value of (-1)"(3n + 2) n=0
Solution: (a) Here, メ)ニ 1+x3 ニ 1-(-x3) ニx2 nニD 3n り=D 3n+2, 3n +2 x)-Eー) x ーIhis rel Ihe (i) り=D haquired power beris representadion of fexy 6) Noo, diffeeren tiading) both Sided of Cis vilh tusfeed to De get 3n +1 (**(1+x*5') = tg"( 3n+2) x*"** nニD の → 2×(1+ッジー(+ッジx= Ee)"en+) x * うゃ)x + 3ntl ラ n=D 3 x4 で+xリー ニ 1+x3
Transcribed Image Text:Solution: (a) Here, メ)ニ 1+x3 ニ 1-(-x3) ニx2 nニD 3n り=D 3n+2, 3n +2 x)-Eー) x ーIhis rel Ihe (i) り=D haquired power beris representadion of fexy 6) Noo, diffeeren tiading) both Sided of Cis vilh tusfeed to De get 3n +1 (**(1+x*5') = tg"( 3n+2) x*"** nニD の → 2×(1+ッジー(+ッジx= Ee)"en+) x * うゃ)x + 3ntl ラ n=D 3 x4 で+xリー ニ 1+x3
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