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)=xsinx 2 -COS nx n -1 -1+ (6) f(x) = xcos x 2n(-1)" sin(nx) (n-1)(n +1) sin nx 0

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Exercise (3-2): find Fourier series on [0,2n]
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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)=xsinx
2
-COS nx
n -1
-1+
(6) f(x) = xcos x
2n(-1)"
sin(nx)
(n-1)(n +1)
sin nx
0<x<A
1-(-1)"
(7) f(x) =
2.
1 A<x< 2n
0<x<T
2ペ-1+(-1)"
sin nx
(8) f(x) =-
1
元くx<2元
1
(9) f(x) =-
3 1-(-1) sin nx
0<xく元
|2 くx<2元
2.
- 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)=xsinx 2 -COS nx n -1 -1+ (6) f(x) = xcos x 2n(-1)" sin(nx) (n-1)(n +1) sin nx 0<x<A 1-(-1)" (7) f(x) = 2. 1 A<x< 2n 0<x<T 2ペ-1+(-1)" sin nx (8) f(x) =- 1 元くx<2元 1 (9) f(x) =- 3 1-(-1) sin nx 0<xく元 |2 くx<2元 2. - 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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