Question

Q1 Given, f(x) = {, 4,05x<2 6x + 1, 2 <x< 4 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks) [Total: 20 marks]

Answer 1

f(x) = { o LT42 xti 2 SI 24 espansion if (o) even half-range sketeh three (3) full period of periodic function in the internal The 5 لمبه 3 2 +2 -11 -10 09 8-7-6-5-4-3-2-1 ALL + 2 3 4s 6 7 ott 9 10 11 12 -2 8 F-4 -6 b cosine coefficient f(*) t ao Ź an cos 2 nar 2 a b = (nap) Jef(x) dx É 1 468) cos (naujas с an 11 + 4 2 a o flo do 11 2 4 2 22 4 dx + 1*2+1) dx [[ue] +<74 . O 2 -In ad 2 ] = 8 [ 8-0 + 8 + 4-2-2

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