Consider the Newton$-$Raphson method to nd a root of an equation. The error Ei is dened

as $($xr $$ xi$)$ where xr is the real $($true$)$ solution. E$0$ is the error of an initial solution x$0.$

Answer following questions.

$($a$)$ How many iteration steps $($n$)$ are required to reduce En to an error threshold $($that

is En $$ $)?$

$($b$)$ Using the answer of $($a$),$ compute the number of the iteration steps required to make

E$0=101$ to En $108.$