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2. Express as a single power series form: Ea,(x– 2)" + (n + 1)a,»,(x – 2)** n%3D2

2. Express as a single power series form: Ea,(x– 2)" + (n + 1)a,»,(x – 2)** n%3D2

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. Test the convergence of the power series below: 00 - (n – 1)2 (2x + 1)" 3"-2 n-1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence 2. Express as a single powerseries form: Ea,x- 2)" +(n + 1)ans1(x– 2)** n=2 n=1 3. Find the Fourier series of, -n<x<-1/2 —п/2 <x <п/2 п/2 <х <л (1 f(x) = }0 4. Determine the Fourier sine series of f(x) = x +1 0<x <n 5. Determine the Fourier cosine series of f(x) = n²– x? 0<x<n 6. For the function y = In (1-x), determine its a. MacLaurin Series expansion up to fifth degree. b. Taylor Series expansion up to fifth degree at xo=0.5
Transcribed Image Text:1. Test the convergence of the power series below: 00 - (n – 1)2 (2x + 1)" 3"-2 n-1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence 2. Express as a single powerseries form: Ea,x- 2)" +(n + 1)ans1(x– 2)** n=2 n=1 3. Find the Fourier series of, -n<x<-1/2 —п/2 <x <п/2 п/2 <х <л (1 f(x) = }0 4. Determine the Fourier sine series of f(x) = x +1 0<x <n 5. Determine the Fourier cosine series of f(x) = n²– x? 0<x<n 6. For the function y = In (1-x), determine its a. MacLaurin Series expansion up to fifth degree. b. Taylor Series expansion up to fifth degree at xo=0.5
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