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Plot the graphs of the odd and even extensions of f. (Clearly indicate the points of discontinuity, if any.) Expand the odd extension of f obtained in part a) in a Fourier Sine Series Fs(r). Find all r E R such that f(r) = Fs(x). Calculate the exact value of Fs(1). %3D Page 1 of 1

Plot the graphs of the odd and even extensions of f. (Clearly indicate the points of discontinuity, if any.) Expand the odd extension of f obtained in part a) in a Fourier Sine Series Fs(r). Find all r E R such that f(r) = Fs(x). Calculate the exact value of Fs(1). %3D Page 1 of 1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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(c) Prove that if x is an eigenvector of a square matrix B, then for any scalar c, x is also an eigenvector of B+ cl. What is the corresponding eigenvalue? 3. Let f(x) = x, 0<x < 1. %3D (a) Plot the graphs of the odd and even extensions of f. (Clearly indicate the points of discontinuity, if any.) (b) Expand the odd extension of f obtained in part a) in a Fourier Sine Series Fs(r). (c) Find all r ER such that f(x) = Fs(x). Calculate the exact value of Fs(1). %3D Page 1 of 1
Transcribed Image Text:(c) Prove that if x is an eigenvector of a square matrix B, then for any scalar c, x is also an eigenvector of B+ cl. What is the corresponding eigenvalue? 3. Let f(x) = x, 0<x < 1. %3D (a) Plot the graphs of the odd and even extensions of f. (Clearly indicate the points of discontinuity, if any.) (b) Expand the odd extension of f obtained in part a) in a Fourier Sine Series Fs(r). (c) Find all r ER such that f(x) = Fs(x). Calculate the exact value of Fs(1). %3D Page 1 of 1
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