1 answer

Given, ?(?) = { 4 , 0 ≤ ? < 2 ? + 1, 2 ≤...

Question:

Given, ?(?) = { 4 , 0 ≤ ? < 2 ? + 1, 2 ≤ ? < 4 (a) Sketch the graph of ?(?) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval −12 < ? < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (c) Write out ?(?) in terms of Fourier coefficients you have found in Q1(b)


Answers

Given solution OS X 32 f(x) = {x41 d<x<4 (a) flxe) 5 fo)=4 4 If y=xth y(2) = 2+123 (23) 404-441= (4.5) 3Ť f(x)2 3+1 2 L I 2 32 of(x) 9 f(x)=x+1 7 5 - (-8,4) (6,4) 4,4) 8.41 (104) o (2,9) 3 2 t + + + 0 2 1 + 6 7 2 3 4 5 -8 7 - 3 -4 -3 ما le ht -24 -343 ao = Ž [ { 4 dx + ( x + 1) an Ž { (4x) + ( x 2 į ( 8 + (432 ++)-( +2)=L(+ = 2 )] 8+8+4-4 il 3 2 5 an = bee 1/2 s f(x) cogni$ by = £ 5 fex) sim More dx = 1/2 f(x) sinnt dat S f(x). sinnte da & Sinne der the+L) sin hrix de 4 2 =*[ $tsimmpex de 15&+1)

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