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PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10 1. Find the radius of convergence and interval of convergence of the power series. an= ant) = (x+2)+ (a) (c) n=0 1 n2n (x+2)" a=2 lim | 0111=1 | −1)″ (3x −1)″ n² n! (x-3)" 02 an ^ √x+2) = 1/2-1/x+2√ = 1 ₂2 (111) ● (n+1)2(+1) (x+1) 2x+1²11x=2 X=1 (+)2

PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10 1. Find the radius of convergence and interval of convergence of the power series. an= ant) = (x+2)+ (a) (c) n=0 1 n2n (x+2)" a=2 lim | 0111=1 | −1)″ (3x −1)″ n² n! (x-3)" 02 an ^ √x+2) = 1/2-1/x+2√ = 1 ₂2 (111) ● (n+1)2(+1) (x+1) 2x+1²11x=2 X=1 (+)2

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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1. C using ratio test

2 PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10 1. Find the radius of convergence and interval of convergence of the power series. TD 12" an= (x+3) ant) - (x+2) =• 4² (n+1) ₂2 (1+1) an (ntl) (x+2)²²a=2 lim /01/2+1/1 = 1 im 2(71) √x+2) = 1/-4x+2) = 호 금 1/2 -1x+²2) = 12x+1²1 1/2 x=2 x=1 (3x - 1)" (a) (b) (c) (d) M8 M8 IM8 IM8 IM 1 n2n n²2 22-1-1 (0*- n! (e) Σ n=0 (x-3)" (n+1)" 3n 1 2n+1 -xn -(x-1) 2n 2. Find the Taylor series of the function f(x) at the point a. (a) f(x) = ²x, a=1 1 (b) f(x) = 1-x (c) f(x) = lnx, 3. Find the Maclaurin series of the function f(x). a=2 a=3 (x+2) ! ++^) (x+2ya (^+1)=2 n
Transcribed Image Text:2 PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10 1. Find the radius of convergence and interval of convergence of the power series. TD 12" an= (x+3) ant) - (x+2) =• 4² (n+1) ₂2 (1+1) an (ntl) (x+2)²²a=2 lim /01/2+1/1 = 1 im 2(71) √x+2) = 1/-4x+2) = 호 금 1/2 -1x+²2) = 12x+1²1 1/2 x=2 x=1 (3x - 1)" (a) (b) (c) (d) M8 M8 IM8 IM8 IM 1 n2n n²2 22-1-1 (0*- n! (e) Σ n=0 (x-3)" (n+1)" 3n 1 2n+1 -xn -(x-1) 2n 2. Find the Taylor series of the function f(x) at the point a. (a) f(x) = ²x, a=1 1 (b) f(x) = 1-x (c) f(x) = lnx, 3. Find the Maclaurin series of the function f(x). a=2 a=3 (x+2) ! ++^) (x+2ya (^+1)=2 n
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