Given function is fx=x0<x≤24-x2<x<4 (a). Given that f is an odd periodic function of period…

Answered: Let х 0

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Let х 0

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter1: Introduction To Algebra

Section1.4: Translating Words Into Symbols

Problem 6MRE

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Question

3. Let
F) =-x 2<x<4
0 <x< 2,
(4-x 2<x<4
a) Consider the odd periodic extension of period T=8, of f(x). Sketch 3 periods on the
interval -12<x<12 of this function.
b) To what value does the Fourier series of this odd periodic extension converge at x=-4 and
X=23?
c) Consider the even periodic extension of period T=8, of f(x). Sketch 3 periods on the
interval -12<x<12 of this function.
а,
, the constant term of the Fourier series of the even periodic function described
2
d) Find
in (c).

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