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6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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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Exercise (3-2): find Fourier series on [0,2n] Question Answer (1) f(x)=x/2 sin nx (2) f(x)= -x sin nx (3) f(x)=sinx sin x (4) f(x) = cos x COS X (5) f(x)=xsin x 2 -COS nx n -1 -1+ 6) f(x)=xcos x 2n(-1)" Σ sin(nx) H(n-1)(n +1) 0<x<A -i-CD sin nx 1-(-1)" (7) f(x) = 2. 1 n<x< 2n 0<x<T 2-1+(-1)" sin nx (8) f(x) =- 1 πくx<2元 0<xく元 3 1-(-1) sin nx (9) f(x) =- 2. |2 くx<2元 - 1/4 (10) f(x)= - T<x<0 1-1+(-1)" sin nx 0<x<A 0<xくて 37 -1)" -1 sin nx (11) f(x) = COS nx- T Tくx<2元 0<x<A sin nx (12) f(x) =- COS NX + 元くx<2元 4 (13) f(x)= 0<x<T (-1)" - COS nx 27-x A<x< 27 T -n
Transcribed Image Text:Exercise (3-2): find Fourier series on [0,2n] Question Answer (1) f(x)=x/2 sin nx (2) f(x)= -x sin nx (3) f(x)=sinx sin x (4) f(x) = cos x COS X (5) f(x)=xsin x 2 -COS nx n -1 -1+ 6) f(x)=xcos x 2n(-1)" Σ sin(nx) H(n-1)(n +1) 0<x<A -i-CD sin nx 1-(-1)" (7) f(x) = 2. 1 n<x< 2n 0<x<T 2-1+(-1)" sin nx (8) f(x) =- 1 πくx<2元 0<xく元 3 1-(-1) sin nx (9) f(x) =- 2. |2 くx<2元 - 1/4 (10) f(x)= - T<x<0 1-1+(-1)" sin nx 0<x<A 0<xくて 37 -1)" -1 sin nx (11) f(x) = COS nx- T Tくx<2元 0<x<A sin nx (12) f(x) =- COS NX + 元くx<2元 4 (13) f(x)= 0<x<T (-1)" - COS nx 27-x A<x< 27 T -n
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