(Solved): Make sure to do all the steps, even the ones where it says to use Desmos to graph. 3. For the (sawto ...

3. For the (sawtooth wave) function $f(x)=\{\begin{array}{ll}-x& -2\le x<0\\ x& 0\le x<2\end{array},f(x+4)=f(x)$ (a) Find the fundamental period. (b) Carefully sketch the graph the function $f$ from $x=-6$ to $x=6$. (c) Find the Fourier series for $f$. (d) Use a computer or graphing calculator or Desmos to graph the sum of the first 5 terms of the Fourier series and see if it's starting to look like the graph of $f$. Draw a rough sketch of what you see. (e) Use a computer or spreadsheet or Desmos to determine the smallest $N$ so that the absolute value of the difference between $f$ and the $N^{\text{th }}$ partial sum of the Fourier series is less than 0.1.