Evaluate teh following limits$.$ Use I:hopital's Rule when it is convenient and applicable.

limx$$x$33\{3$x$$sin$3$x$\}\backslash$lim$\_\{$x$\backslash$to$\backslash$infty$\}\backslash$frac$\{$x$^3\}\{3\}\backslash$left$\backslash \{\backslash$frac$\{3\}\{$x$\}-\backslash$sin$\backslash$frac$\{3\}\{$x$\}\backslash$right$\backslash \}$limx$$$3$x$3\{$x$3$sinx$3\}$

$3$x$+3\backslash$frac$\{3\}\{$x$\}+3$x$3+3$

on $[1,5],$ n$=4$