Consider P$\backslash$infty

n$=0$

x$3$n

$(3$n$)!,$ that is$,$ the power series obtained by keeping every third term in the

Taylor expansion of exp$($x$).$ This power series corresponds to the true function

ftrue$($x$)=1$

$3$ exp$($x$)+2$exp$($x$/2)$ cos

$3$x

$2$

$!!$

For any possible integer k$,$ define the k term power series approximation fapprox$($x$,$ k$)$ :$=$

Pk$1$

n$=0$

x$3$n

$(3$n$)!.$

Submit a MATLAB code $(.$m file$)$ named YourlastnameYourfirstnameHW$2$p$2.$m that plots

$2$D line plots for the functions ftrue $($in black solid line$)$ versus x in $[5,5]($in the horizontal

axis$).$ In the same figure window, plot fapprox$($x$,$ k$)$ for k $=2($in red dashed line$),$ k $=3($in

green dashed line$),$ k $=4($in blue dashed line$).$

We shared a starter code YourlastnameYourfirstnameHW$2$p$2.$m inside the the CANVAS File

section Files$/$MATLAB Files$/$Homework $2.$ You only need to complete lines $11$ and $20$ in that

starter code, then rename the file appropriately with your first and last names