The function $f(x)=e^x$ can be evaluated using the following infinite series:

$(x)=e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+$cdots

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

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

${}_a<msub\; id="EditorElement\_3205938"><mrow><mi\; id="EditorElement\_3205931"></mi></mrow><mrow\; id="EditorElement\_3205937"><mi\; id="EditorElement\_3205934">s</mi></mrow></msub>$ 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 $x=3,{}_s=1{10}^{-5}\%$ 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 $=20\mathrm{.}0855$

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

terms $=18$