Show detailed steps for both problems

$1.$ Illustrate the Bisection Method to solve the following equation for a root. Try the following guesses to solve.

Eqn to be solved:

f$($x$)=$ x$27$

a$.$ Guess a $=2\mathrm{.}0,$ b $=3\mathrm{.}0$

b$.$ Guess a $=-2\mathrm{.}0,$ and b $=-3\mathrm{.}0$

In both cases take the accuracy to be $0\mathrm{.}001$

$2.$ Given, f$($x$)=3$x $+$ sin$($x$)$ ex $=0$

Use Newton$-$Raphson method to determine the roots of the function, derivatives of sin$($x$)$ is cos$($x$)$ and derivative of ex is ex

a$)$ Use X$0=0$

b$)$ Use X$0=1\mathrm{.}5$

In both cases use accuracy of $0\mathrm{.}001$

How many iterations took in each case?