Suppose that f(t) is periodic with period |-, 7) and has the following real Fourier coeficients: do - 4, a, -1, az- 3, ag - 3, b = 2, b = -3, bg = 0, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3) {(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coeficients for the following functions: (1) The derivative f'(t) a --1 -6 ... b, - 2 by -6 (H) The function f(e) – 2 de =0 3 3 ... b,-2 -3 by (iii) The antiderivative of (f(t) – 2) (with C = 0) 1 3/2 ... -2 by 3/2 (iv) The function f(t) + 3 sin(3t) +3 cos(2t) đo = 2 1 6. 3 b,-2 by -3 by -3 (Iv) The function f(2t) 2 1 3 3 ... 2 bz -3 by

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