Exercise $1.$ Write a short program to interpolate the hat function

$f(x)=\{\begin{array}{cc}x,& x\\ -x,& x>\end{array}$

by trigonometric polynomials for $l=2,4,8,16,$ and $32.$ Measure maximum absolute error on the mesh $0$:$\mathrm{.}01**$:$2**$ and observe improvement that ip only linear in $l($or $n=2l-1).$