Problem # $2$: For each of the three cases in problem #$1$ above, find the error involved in approximating $f$ with the corresponding Fourier series when $x=4,$ and the series is truncated after $7$ terms.

$($Note that the error is defined to be the absolute difference between the actual $f$ value and the approximate $f$ value.$)$

The definite integrals appearing in the series should be evaluated numerically using the function trapz. For this purpose the interval $0,8$ should be discretized using $200$ subintervals.

Enter the errors for $($a$),($b$),$ and $($c$),$ in that order, into the answer box below, separated with commas.