A function f(x) is given on the interval 0 < x < L, f(x)=3x, 0...

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A function f(x) is given on the interval 0 < x < L, f(x)=3x, 0<x<3. (a) Sketch the graph of the even extension feven (x) of period 2L and the graph of the odd extension fodd(x) of period 2L. (b) Find the Fourier cosine series for feven with period 2L. (c) Can we find the Fourier sine series for feven with period 2L? why? A function f(x) is given on the interval 0 < x < L, f(x)=3x, 0<x<3. (a) Sketch the graph of the even extension feven (x) of period 2L and the graph of the odd extension fodd(x) of period 2L. (b) Find the Fourier cosine series for feven with period 2L. (c) Can we find the Fourier sine series for feven with period 2L? why?