Here is a Taylor Series: $,$ valid for

$.$

$($a$)$ Write a local function $($within the same function file $--$ see the template below$)$ function z$=$my$\_$fact$($a$)$ that computes the factorial of a number, e$.$g$.$:

$.$ Do not use MATLAB's built$-$in factorial function, build your own from scratch, possibly but not necessarily using using a for loop. $($Pro$-$tip, you can still compare the results of your function to MATLAB's in the command window to confirm it is working right.$)$

$($b$)$ The main function will be function $[$y$,$err$]=$trunc$\_$err$($x$,$N$)$ which has as inputs: x$,$ the value plugged$-$in to the above expression; and N$,$ the number of terms in the Taylor Series. The outputs of this function are y$,$ the evaluation of the Taylor Series at x through N terms; and err, the truncation error of the Taylor Series. You may use MATLAB's built$-$in sqrt to determine the "true value", and should report the err as a relative error $($as a decimal, not a percentage$).$