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4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0

4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0

Advanced Engineering Mathematics
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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Formula is given first find bn and then put on formula 

HALF RANGE SINE SERIES Suppose that f(x) satisfies Dirichlet's condition in the interval 0 <x < t f(x) is an even function of period 2t, then even periodic G(x) will have a convergent Fourier series representation consisting of cosine terms only and given by 00 NITX G(x) = ) bn sin n=1 b, =5 f(x)sin™ ппх dx,(n = 0,1,2, ..)
Transcribed Image Text:HALF RANGE SINE SERIES Suppose that f(x) satisfies Dirichlet's condition in the interval 0 <x < t f(x) is an even function of period 2t, then even periodic G(x) will have a convergent Fourier series representation consisting of cosine terms only and given by 00 NITX G(x) = ) bn sin n=1 b, =5 f(x)sin™ ппх dx,(n = 0,1,2, ..)
4. Find the half-range Fourier cosine series for the function f(x)=sinx in the range 0<x<n Sketch the function within and outside of the given range. 5. Find the half-range Fourier sine series for the function f (x)=x in the range 0<r<3.Sketch the function within and outside of the given range.
Transcribed Image Text:4. Find the half-range Fourier cosine series for the function f(x)=sinx in the range 0<x<n Sketch the function within and outside of the given range. 5. Find the half-range Fourier sine series for the function f (x)=x in the range 0<r<3.Sketch the function within and outside of the given range.
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