Consider the following function: -- 2, -2 < r <-1 f(x) = {1, 2-z, 1

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
Chapter8: Introduction To Functions
Section8.7: Functions Defined By Equations
Problem 9WE
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4. Consider the following function:
-r- 2, -2 <I<-1
f(r) = {1,
-1<r<1
2-1,
1<r< 2.
(i) Sketch the graph of f and find its Fourier series on [-2, 2).
(ii) Use the obtained series to deduce that:
1.
1
and E
(2k – 1)²
(2k – 1)
8
96
k=1
Transcribed Image Text:4. Consider the following function: -r- 2, -2 <I<-1 f(r) = {1, -1<r<1 2-1, 1<r< 2. (i) Sketch the graph of f and find its Fourier series on [-2, 2). (ii) Use the obtained series to deduce that: 1. 1 and E (2k – 1)² (2k – 1) 8 96 k=1
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