$cos(x)={\displaystyle \underset{i=0}{\overset{n}{}}}(-1{)}^i\frac{x^{2i}}{(2i)!}$ is the Taylor $/$ McClaurin expansion of order $n,$ centred at $x=0$ for $cos(x).$

$($a$)(10$ points$)$ Write a Matlab program that computes the n$\text{'}$th order expansion and plots this expansion and the real values of $cos(x)$ on the interval $-$

Hints : try modifying the code snippet for computation of the Maclaurin expansion of $sin(x)$ given in the week $6$ lecture notes!

$($b$)(3$ points$)$ Modify your code to compute and plot the error between the expansion and the real value of $cos(x)$ for all xin$[-,]$

$($c$)(2$ points$)$ Add commands to your code to compute the sum of the squared errors and comment on what happens to this as the order $n$ of the expansion is increased.