$10$ pts$)$ Sort the following functions in terms of asymptotic growth from smallest to largest. In

particular, the resulting order f$1,...,$ f$12$ should be such that f$1=$ O$($f$2),$ f$2=$ O$($f$3),$ and so on$.$

Identify any groups of functions that are $\backslash$Theta of one another.

n $2$n n$3$ n ln$($n$)2$ n$!$ log$2((4$n$)$n$)$ ln$($n$2)(3$

$2$

$)$n n$1/5$ ln$2($n$)52!$