Use lim$($n $->\backslash$infty $)($f$($n$))/($g$($n$))$ to establish proof or disproof. Is $$n$2^$n growing faster than the exponential function $2^$n $?[$Hint: Use lim$($n $->\backslash$infty $)2^$n$/($n$2^$n $)$ to show your claim.$]$ What is the order of growth if the closed$-$form formula is $$n $2^$n$?$ Prove or disprove $3^$n has a smaller order of growth than $2^2$n$.$ What is the order of growth if the closed$-$form formula is $2^2$n$?$ Prove or disprove $($n$-2)!$ is faster growth than $2^2$n$.$ What is the order of growth if the closed$-$form formula is $($n$-2)!?$