Using MATLAB Develop a computer program that uses the Newton$-$Raphson method to calculate the roots of a given function. Then use the program to calculate the positive root of each of the following functions.a$.$ f$($x$)=0\mathrm{.}51$ x sin$($x$)$b$.$ f$($x$)=$ x$101$For each case, obtain and present the following results$\mathrm{.}1.$ Plot of the function over an appropriate range to show the root$\mathrm{.}2.$ Tabulate the results for the first $50$ iterations showing i $($iteration no$.)$ x$($i$)\%$ relative error$\mathrm{.}3.$ Computer$-$generated plot of the root estimate as a function of iteration number$\mathrm{.}4.$ Computer$-$generated plot of the $\%$ relative error as a function of iteration number$\mathrm{.}5.$ Explain the reason for the dramatic difference in convergence rate for the two cases$\mathrm{.}6.$ Program listing $($so the professor or assistant can duplicate results$-$if needed$).$For case $($a$)$ use an initial guess of x$=1\mathrm{.}5$ and for Case $($b$)$ use an initial guess of x$=0\mathrm{.}5.$