Suppose that f(t) is periodic with period [-a, *) and has the following real Fourier coefficients: ao = 4, a1 = 1, az = 3, az = 3, b = 2, by = -3, by = 0, .. (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative '(t) -6 b, = b = -6 b = (1) The function f(t) – 2 ag = .... b, = , b = by = (iii) The antiderivative of (f(t) – 2) (with C = 0) 3/2 az = b, = by= 3/2 by %3D (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) do 1 , ds = 3 .... b, =2 b2 =-3 3 (iv) The function /(2t) , ag = bz =

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