Question $1$: For each pair of functions below, first determine which function grows asymptotically faster,

and then express the relation between the two functions using all the asymptotic notations and $)$

that apply. Only give the relations in which $f(n)$ appears on the left$-$hand side.

$(1)f(n)=n^2+(logn{)}^3,g(n)=n^{2}logn$

$(2)f(n)=3^n$

$g(n)=2^n+n$

$(3)f(n)=4^n$

$g(n)=4^{n+3}$

$(4)f(n)=6n^3+7n^2+2$

$g(n)=n^3$

$(5)f(n)={\displaystyle \underset{i=0}{\overset{k}{}}}{n}^i$

$g(n)=n^{k+1}$

please answer all of these questions and make sure the final answeris correct Please make sure to answer all of them thank you