mplement the Newton divided difference algorithm $($Page $332$ in the textbook, section

$6\mathrm{.}2$ with subtitle $$Algorithm for Divided Difference$)$ together with the nested multiplication

algorithm $($Page $310$ in the textbook$).$ Then use your code to find the Newton interpolating

polynomial pn for the function f $($x$)=1/(1+$ x$2)$ on the interval $[5,5]$ for n $=5,10$ and $15.$

In each case, use a smaller spacing $($e$.$g$.$x $=0\mathrm{.}1)$ to draw the graph for f $($x$)$ pn$($x$)$ with

x in $[5,5].$ What do you observe