Root finding in one dimension: We want to compute the roots of the equation to a

tolerance of ${10}^{-3}.$

$f(x)=e^x-x^2$

It is known that the roots of the equation lie between lower and upper bound, $-2,2.$ Do all

calculations by hand upto $3$ iteration. Show details of all calculations. Create a table showing

the progress of your calculation by iteration number.

$($a$)$ Use the Bisection method to solve for the root.

$($b$)$ Use the Regular$-$Falsi method to solve for the root.

$($c$)$ Use the Newton Raphson to solve for the root. Use an initial guess of $-2.$

NOTE $1$: For Bisection$/$Regular$-$Falsi method you should create a table that shows the

following columns, iteration no$.,x_1,x_2,x_3,f(x_1),f(x_2),$ and $f(x_3).$ For Newton$-$Raphson

method that columns should be iteration no$.,x_1,$ and $f(x_1).$