$($Strange behavior of a continuous function: LM $3\mathrm{.}1-25)$ Consider the function

$f(x)=\{\begin{array}{ccc}\frac{e^x-1}{x}& if& x0\\ 1& if& x=0\end{array}$

This is a continuous function for all xinR, but numerically it has difficulties when $x$~~$0.$

$($a$)$ Check this yourself by letting $x={10}^{-k}$ for $k=1,2,$dots,$15.$ Generate a nice table using

either disp or fprintf. Do it without using any loop.

$($b$)$ Repeat the previous part but rewrite $f(x)$ as

$f_2(x)=\{\begin{array}{ccc}\frac{e^x-1}{log{e}^x}& if& x0\\ 1& if& x=0\end{array}$

which was proposed by Bill Kahan. Leave the denominator as $log{e}^x-$ do not convert

it to $x.$ Do it without using any loop.

$($c$)$ Summarize the results of the two parts into a single table. The table should have three

columns with the first being $x,$ the second being $f(x),$ and the last being $f_2(x).$ Use

format long $g$ for your output if using disp; use a compatible format specification

if using fprintf. Do it without using any loop.

Note. Write your code inside a single code block for each part. You do not need to write a

function for this problem.