$3.$ Develop a MATLAB function to compute the Maclaurin series expansion for the cosine function given

as:

$cosx={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n)!}{x}^{2n}=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+$cdots

Test your program for: $=\frac{}{3}(60)$ and $=\frac{7}{3}(420).$

The first line of the function should be:

function $[$fx$,$ea$,$et$,$iter$]=$ Lastname$\_$Cos$($x$,$es$,$ maxit$)$

Note: Pattern your function according to the sample in Fig. $4\mathrm{.}2.$ Be sure to calculate the et value also.

$4.$ the velocity of a rocket might be described by:

$v(t)=\{\begin{array}{cc}10t^2-5t,& 0t8\\ 624-3t,& 8t16\\ 36t+12(t-16{)}^2,& 16t26\\ 2136e^{-0\mathrm{.}1(t-26)},& t>26\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

First, develop a function file $($using the if $...$ else structure$)$ with the first line:

function $v=$ Lastname$\_$Vel $(t)$ to compute velocity as a function of time for each interval.

Then, write a script named as Lastname$\_$Call$\_$Vel that uses the function to generate a plot of $v$

versus $t$ for $t=-5$ to $50.$ Label your plot accordingly.

Hint: You will need a loop to create the corresponding values of $t$ and $v,$ where $v$ is based on the

function you created.

Note: Do NOT use the built$-$in piecewise function for this problem.

Also, ensure that each MATLAB file is named appropriately, starting with your last name.