$3\mathrm{.}16$ Write a MATLAB user$-$defined function that solves for a root of a nonlinear equation $f(x)=0$ using

the bisection method. Name the function Xs $=$ BisectionRoot$($Fun$,a,b).$ The output argument Xs is

the solution. The input argument Fun is a name for the function that calculates $f(x)$ for a given $x($it is a

dummy name for the function that is imported into BisectionRoot$)$; a and $b$ are two points that

bracket the root. The iterations should stop when the tolerance in $f(x)($Eq$.(3\mathrm{.}5))$ is smaller than $0\mathrm{.}000001.$

The program should check if points a and $b$ are on opposite sides of the solution. If not, the program

should stop and display an error message. Use BisectionRoot to solve Problem $3\mathrm{.}2.$

problem $3\mathrm{.}2$: Determine the root of f$($x$)=$ x$-2$e$^(-$x$)$ by:

a$)$ using the bisection method. start a $=0$ and b $=1,$ and carry out the first three iterations.

b$)$using the secant method. Start with the two points, x$1=0$ and x$2=1,$ and carry out the first three iterations.

c$)$using the Newton's method. Start x$1=1$ and carry out the first three iterations.