Can someone help me with those question please. I really appreciate for your help. Explain with step by step please.

PART $2-$ Comparing the orders of growth between two algorithms $(4$pts$)$

Say we have two different algorithms with respective runtimes of $f(n)$ and $g(n).$ Given the

following cases, prove whether or not $f(n)$ is $O(g(n))$ in each case.

You need to show your work with the crucial steps, e$.$g$.$ finding the necessarily constant c in the

definition of Big$-$O$.$ You may utilize the pull$-$up$/$pull$-$down or the l'Hopital's trick discussed in class

whenever needed.

You will be penalized for up to $1pt$ in total if all your work for this entire PART exceeds a whole

$A\frac{4}{?}$ US letter page in $12px$ font size $($assuming you start from the top of the page$).$

P$.$S$.$ sqrt$($n$)$ means the square$-$root of $n,$ aka $n^{{?}^{{?}^{?}}}(\frac{1}{2}).$