Please Solve Consider the equation: f$($x$)=$ x

$22$x $3+$ e

x $=0.$

a$)$ Use the Newton$-$Raphson method to find the root of above equation. Employ an initial guess of x$0=1$

and repeat iterations until three digits after the decimal have converged.

b$)$ Repeat the exercise with false position method, using the bracket $(0,2).$ Use the same convergence criterion

as before.

c$)$ Which method converges faster $?$

Only handwritten work needs to be submitted for this HW$.$ Show all iterations clearly in a table format. Please

draw a line after the end of each part $($and the beginning of next$),$ so your solutions for each part can be easily

identified.