. Find Fourier series of the following functions on the interval [-1, 1]: a) f(x) = sin(6r), b) f(x) = sin() c) f(x) = 1 d) f(x) = x² e) f(x) = 1+ x2 S1 (1 xE|-1,0] f) f(x) = || те (0, 1] so 0 xE [-1,0] g) f(x) ле (0, 1]

Consider f(x) = sin(x²). Is the function even, odd or neither, and which conse- quence does the answer have for its Fourier series?

= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.

2 Denote the Fourier series of f(z) = { -x, 0