Question 2 (a) (i) Compute the cosine Fourier series of the function g(x) = 1, 0≤x≤2 What can you say about the coeffici

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Question 2 A I Compute The Cosine Fourier Series Of The Function G X 1 0 X 2 What Can You Say About The Coeffici 1 (33.87 KiB) Viewed 38 times

Question 2 (a) (i) Compute the cosine Fourier series of the function g(x) = 1, 0≤x≤2 What can you say about the coefficients a,, when ʼn > 0 is even? You may find the following formulas useful [x cos(az) dz = sin(ar) + cos(ar) + C₁ sin(n) = 0. (ii) Find the coefficients of the cosine Fourier series of the function h(x) = sin(x), 0≤I≤ 2. You may find the following formulas useful cos(br) sin(ar) dx = -(con((a+b)x)+ con((a-b)x)) + C cos(az) sin(ar) dr = cos (20x) 4a cos(±a ± 2) = cos(a), cos(n) = (-1)", +C Show that a = 2 and that for n ≥ 1 0≤x≤2 a> 0, What can you say about the coefficient a,, when ʼn is even? [4 marks] (iii) Explain briefly how you would use parts (i) and (ii) in order to compute the coefficients a,, of the cosine Fourier series of the function f(x)=x-sin(x), { P(-²) 21 odd n 21 even. [4 marks] if a, b>0 and ab. if a > 0, [2 marks]