g$\_(5)=$n$^(8\mathrm{.}2)+$n $!$

g$\_(6)=$n$^(2024)+$n$^(512)+$n$\backslash$times log$($n$)$

g$\_(7)=$e$^($n$)+$e$^($ln$($n$))$

g$\_(8)=\backslash$sqrt$($log$($n$))$

Tip: Work in stepwise format. Find the fastest growing function first, and then the next fast one

Asymptotic Notations $(6$ points$)$ For each pair of the following functions f$($n$)$ and g$($n$),$ check if

f$($n$)=\backslash$theta $($g$($n$))?$

f$($n$)=$O$($g$($n$))?$

f$($n$)=\backslash$Omega $($g$($n$))?$

f$($n$)=$o$($g$($n$))?$ Little o$?$

f$($n$)=\backslash$omega $($g$($n$))?$ Little omega?

Functions f$($n$)$ and g$($n$)$ are:

f$($n$)=(128)^((($n$)/(4)))$ vs$.$ g$($n$)=(512)^((($n$)/(8)))$

f$($n$)=$n$^(64)\backslash$times $2^($n$)$ vs$.$ g$($n$)=$log$($n$)\backslash$times $2^($n$)+4^($n$)+$n$^(32)$

f$($n$)=$n$^(1024)$ vs$.$ g$($n$)=2^($log$($n$)\backslash$times log$($n$))$

You do not need to provide a formal proof. Describe your justifications in text form.