(a). The Fourier series of a function f(x) is defined as ao f(x) = 40 +...

 

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(a). The Fourier series of a function f(x) is defined as ao f(x) = 40 + (an cos (27727) + bn sin (247) 2 n=1 With a = = SX0+ f(x) cos (77x) dx, b, = SXo+ (x) sin (x) dx Jxo where L is the period and xo is arbitrary. (i). Find the Fourier series of the function f(x) = x with period 2 for - < xn.[7] (ii). Hence show that 714 11 113 1 1 5-7 [41. (a). The Fourier series of a function f(x) is defined as ao f(x) = 40 + (an cos (27727) + bn sin (247) 2 n=1 With a = = SX0+ f(x) cos (77x) dx, b, = SXo+ (x) sin (x) dx Jxo where L is the period and xo is arbitrary. (i). Find the Fourier series of the function f(x) = x with period 2 for - < xn.[7] (ii). Hence show that 714 11 113 1 1 5-7 [41.