Consider the function

$F(h)=\frac{h-sin(h)}{h^3}$

where $h$ is a positive value. It is not possible to evaluate this function when

$h=0$ due to a division by zero error. In order to understand the behaviour

of this function as $h$ approaches zero, we can calculate $F(h)$ for a series of

smaller and smaller values of $h$ and observe the resulting output values.

$($a$)$ Write a Matlab code that computes the function $F(h).$

Then, create a plot of $F(h)$ for a range of $h$ values $.$

By using different values of $h,$ estimate the limit of $F(h)$ as $h$

approaches zero.

Consider the possibility that $h$ may be chosen too small and

explain what can happen in this scenario.

Explain your reasoning. Remember to choose appropriate scales for

the axes in your plot.

$($b$)$ Showing your work, find the limit $L=\underset{h0}{lim}F(h)$ analytically.

Then, create a plot of $|F(h)-L|$ for various $h.$

We are interested in the largest value of $p$ for which

$F(h)=L+O(h^p).$ Using your plot, find $p.$

Explain your reasoning. Remember to choose appropriate scales for

the axes in your plot.Please make a report and do matlab code and post screenshot Your report cannot exceed one page. It should include at least one figure

with proper labels. Make sure to choose axis scales appropriate for the

data. Discussions should be kept brief and answer all questions asked.