Q3(a) A periodie system can be approximately represented by the following function: 2, -4 ...

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Q3(a) A periodie system can be approximately represented by the following function: 2п, -4п < х<-п f(x) = {-2x, (-27, n<x< 4n (i) Sketch three periods of the function between -12n to 12n. Explain whether the function is even, odd, or neither. (6 marks) (ii) Find the Fourier series of f(x). (9 marks) (b) Combine the following power series into a single power series with power x". by applying the index shifting approach. 3x2 п(п — 2)(п — 1)х"-5 + 2х n xn-2 n=5 n=3 (5 marks) Q3(a) A periodie system can be approximately represented by the following function: 2п, -4п < х<-п f(x) = {-2x, (-27, n<x< 4n (i) Sketch three periods of the function between -12n to 12n. Explain whether the function is even, odd, or neither. (6 marks) (ii) Find the Fourier series of f(x). (9 marks) (b) Combine the following power series into a single power series with power x". by applying the index shifting approach. 3x2 п(п — 2)(п — 1)х"-5 + 2х n xn-2 n=5 n=3 (5 marks)