Below the problem is the starter code A function and its approximations $(30$ points$)$ Consider $\_$n$=0^\backslash$infty 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

f$\_$true $($x$)=1/3($exp $($x$)+2$ exp $(-$x $/2)$ cos$((3)$ x$/2)).$

For any positive integer k$,$ define the k term power series approximation f$\_$approx $($x$,$ k$)$:$=\_$n$=0^$k$-1$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 f$\_$true $($x$)($in black solid line$)$ versus x in $[-5,5]($in the horizontal axis$).$ In the same figure window, plot f$\_$approx $($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 YourlastnameYourf irstnameHW$2$p $2.$m inside the CANVAS File section folder: HW Problems and Solutions. You only need to complete lines $11$ and $20$ in that starter code, then rename the file appropriately with your first and last names. Hint: Look up sqrt$,$ exp, cos$,$ sum, factorial, and power $(.)$ in MATLAB documentation. Also, intuition suggests that as k increases, f$\_$approx should get close to f$\_$true.