Question $5[10$ points$]$ Consider computing the interpolating polynomial $P_n(x)$ for the function

$f(x)=\frac{1}{2+cos(x)}$

with a uniformly spaced subdivision of the given interval $a,b.$ Study the interpolating polynomial and

its errors for the intervals $0,2$ and $-,,$ for varying $n.$

For the interval $0,2,$ write a Matlab code to simultaneously plot the functions $f$ and $P_n$ for

$n=5,10$ on a single figure. Then, create a separate figure to plot the error functions $f-P_n$ for

$n=5,10.$

Apply the instructions from Question $5\mathrm{.}1$ to the interval $-,$ and for $n=5,10,15,20.$

You can use Matlab build$-$in functions 'polyfit' and 'polyval' for polynomial interpolating and evaluating.