(Solved): please solve all Suppose \( f(x) \) has Fourier series \[ \frac{1}{2}+\sum_{k=1}^{\infty} \frac{2}{( ...

Suppose \( f(x) \) has Fourier series \[ \frac{1}{2}+\sum_{k=1}^{\infty} \frac{2}{(2 k-1) \pi} \sin ((2 k-1) x) . \] (a) What is the period of \( f \) ? (b) What is the average value of \( f(x) \) on the interval \( [-\pi, \pi \) (c) What is \( \int_{-\pi}^{\pi} f(x) \cos (3 x) d x \) ? (d) \( \int^{\pi} f(x) \sin (3 x) d x \) ?