Consider f$($x$)=$ r $1/$x $.$

a$)$ Use the Newton$$Raphson method to show that xn$+1=2$xn $$r$($xn$)^2.$

b$)$ Determine by iteration$($s$)$ the root of f$($x$)$ when r $=12$ correct to five decimal places. Choose our starting iteration to be x$0=0\mathrm{.}1.$