(b) You are given that the Fourier series for f on the interval (-7, 7) is [a, cos(nx) + b, sin(nx)]. n=1 Explain why b, = 0 for n = 1, 2, 3, ... , and find a,, for n = 0, 1, 2, ..

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let f(x)=|x| , -pi
(a) Sketch the graph of the 27-periodic extension of f for -47 < r < 4n.
(b) You are given that the Fourier series for f on the interval (-7, 7) is
ao+[a, cos(nx) + b, sin(nx)] .
2
n=1
Explain why b, = 0 for n = 1, 2, 3, .., and find a,
for n = 0, 1, 2, ..
Transcribed Image Text:(a) Sketch the graph of the 27-periodic extension of f for -47 < r < 4n. (b) You are given that the Fourier series for f on the interval (-7, 7) is ao+[a, cos(nx) + b, sin(nx)] . 2 n=1 Explain why b, = 0 for n = 1, 2, 3, .., and find a, for n = 0, 1, 2, ..
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