The Fourier series for f(x). f(x) = 2 + Σ (ancos 7x + b₂ sinx) bn n=1 is of the form f(x) = co + (8₁(n,x) + g₂(n,x)) Σ n = 1 (a) Find the value of co. (b) Find the function gi(n,x). (c) Find the function g2(n,x).

Consider the piecewise function x, -2 0. (v) Find the simplified general expression for the Fourier coefficients bn, n > 0. (vi) What is the Fourier series F(x) of f(x)? (vii) What value will the Fourier series compute to at x = 18? viii) What is the overall convergence rate of the Fourier series?

Consider the Fourier expansion = (−1)²k+1 . 2 k ∞ f(x) = [ck · sin(kx), k=1 where Ck = Describe the periodic function f(x). Verify that the first Fourier coefficient satisfies C1 = CTT -π xsin (x) dx.

Find the cosine Fourier coefficients for the function f(x) = 35 cos(3x), on 0Sxs. O A None of these. 140 and an- 35 (-1)+1 (-1)" 2n+3 2n-3 O B.40 =- 37 n=1,2,3,... 140 and an- 70 (-1)+1 (-1)" 2n +3 Oca0 =- 2n-3 n=1,2,3,... 140 and an= 元 70 (-1)*1 2n +3 (-1)" 2n-3 O Da0 =- n = 1,2,3,... %3D 70 (-1)+1 (-1)" 2n-3 2n+3 n= 0,1,2,3,... OE an=