Question $1(50$ marks$)$:

For the following Maclaurin series:

$cosx={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n)!}{x}^{2n}=1-\frac{x^2}{2!}+\frac{x^4}{4!}-$cdots

i$.$ Write a MATLAB function, named my$\_$fun, that will accept $x$ and $N$ as inputs and produce one output, corresponding to the approximated value of $cos(x)$ given in the equation above. You must use for$-$loops.

ii$.$ Test your function for $x=0\mathrm{.}3$ and $N=3$ and store the result in a variable named test$\_$fun.

iii. For $x=0\mathrm{.}3,$ call the $m{y}_{-}$fun function six times, corresponding to $N=0,1,2,3,4$ and $5.$ Use a for$-$loop to solve this part and store the result of the function calls in an array named test $2$ fun.

iv$.$ Plot a bar graph showing the absolute error difference between the results for all calls and the actual value of $cos(x).$ Add a descriptive title and labels.

v$.$ Compare your performance for both functions using $)=0\mathrm{.}5,N=(10.$ Call each function $100$ times and time them using the commands tic and toe.