# Fourier series for $2x - x^2$; going from a table to a Fourier series

Q1. (a) Find the Fourier series of periodicity 3 for $f (x) = 2x-x^2$ in $0<x<3$.

(b) The table of values of the function $y=f(x)$ is given below: $$\begin{array}{rcrcrcrcrcrcrcr} x:&\quad&0&\quad& \pi/3&\quad& 2\pi/3&\quad&\pi&\quad&4\pi/3&\quad&5\pi/3&\quad&2\pi\\ y:&& 1.0&& 1.4&&1.9&& 1.7&& 1.5 && 1.2&& 1.0 \end{array}$$ Find a Fourier series up to the second harmonic to represent $f(x)$ in terms of $x$.