1. Find the Interval, Radius and Center of Convergence. n 2n n=0

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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CHALLENGE PROBLEMS
1. Find the Interval, Radius and Center of Convergence.
Σ
2n
n=0
2. Add or subtract the following power series:
E na,x"-1 + x anx"
X
n=1
n=0
3. Find the Taylor series expansion of f(x) = xe* centered at xo = 0, up to
fifth degree.
4. Define the Maclaurin series of the function, up to fifth degree:
y = sin x
5. Find the Fourier Series of the function:
S0,
-T < x < 0
f(x) =
1,
0 <x< T
6. Find the sine series of
{ -
0 < x < T/2
T/2<x < T
X,
f(x)
п - х,
Transcribed Image Text:CHALLENGE PROBLEMS 1. Find the Interval, Radius and Center of Convergence. Σ 2n n=0 2. Add or subtract the following power series: E na,x"-1 + x anx" X n=1 n=0 3. Find the Taylor series expansion of f(x) = xe* centered at xo = 0, up to fifth degree. 4. Define the Maclaurin series of the function, up to fifth degree: y = sin x 5. Find the Fourier Series of the function: S0, -T < x < 0 f(x) = 1, 0 <x< T 6. Find the sine series of { - 0 < x < T/2 T/2<x < T X, f(x) п - х,
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