Prove that lg $($n$!)$ in $\backslash$Theta $($n lg n$).$ Also prove that n$!$ in $\backslash$omega $(2^$n$)$ and n$!$ in o$($n$^$n$).$ Hint: Use Stirling$$s approximation: n$!=$ sqrt$(2\backslash$pi n$)($n$/$e$)^$n $(1+\backslash$Theta$(1/$n$))$