The function $()=$ can be evaluated using the following infinite series:

$()==1++$

$$

$2!$

$+$

$$

$3!$

$+$

$$

$4!$

$+$

Create a function m$-$file called Lab$1$Q$3.$m that evaluates the function to a certain error

tolerance s

$($i$.$e$,$ continues adding terms one at a time until the approximate percent relative

error$$ a $$ s $).$

The input variables to the function should be x $,$ s

$$ and the maximum number of terms

maxterms. In case the solution will not converge, it is always a good idea to specify a

maximum number of iterations or terms such that the code will terminate when either

a s $$ or the number of terms reaches the maxterms value.

The output variables should be the result of the function $($funcex$),$ the approximate error after

convergence is reached $($ a $),$ and the number of terms required for the solution to converge

$($terms$).$ The first line of the function should therefore be as follows:

function $[$funcex$,$ea$,$terms$]=$Lab$1$Q$3($x$,$es$,$maxterms$)$

Test this function for x $3,$ s

$1$ x $10-5\%$ and maxterms $=100$ using the following command

in Command Window:

$[$funcex$,$ ea$,$ terms$]=$Lab$1$Q$3(3,1$e$-5,100)$

The solution should be:

funcex $=20\mathrm{.}0855$

ea $=1\mathrm{.}8076$e$-6$

terms $=18$