### $4.$ Fixed Point Method

Use simple fixed point iteration to locate the root of $f$\_4($x$)=2$ sin$(\backslash$sqrt$\{$x$\})-$ x$$.$ Use an initial guess of $x$\_0=0\mathrm{.}5$$ and iterate until $$\backslash$epsi $\_$a $0\mathrm{.}01\backslash \%$$$.$

$-$ save the root on $***$HW$3\_9.$dat$***$ file

$-$ save the estimated error $$\backslash$epsi $\_$a$ on $***$HW$3\_10.$dat$***$ file