For each of the following pairs of functions $f(n)$ and $g(n),$ decide whether we have $f(n)=(g(n))$

$f(n)=O(g(n)),$ or $f(n)=(g(n))$

If $f(n)=(g(n)),$ you will not earn any point by selecting $f(n)=O(g(n))$ or $f(n)=(g(n)),$

since $f(n)=(g(n))$ tells more than each of the other two.

Q$1\mathrm{.}1$

$2$ Points

$f(n)=n^{2}lnn$

$g(n)={\displaystyle \underset{i=1}{\overset{n}{}}}i$

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

$f(n)=(g(n))$

$f(n)=(g(n))$

Q$1\mathrm{.}2$

$2$ Points

$f(n)={1\mathrm{.}001}^n$

$g(n)=n^{1\mathrm{.}001}$

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

$f(n)=(g(n))$

$f(n)=(g(n))$

Q$1\mathrm{.}3$

$2$ Points

$f(n)=2n!$

$g(n)=(2n)!$

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

$f(n)=(g(n))$

$f(n)=(g(n))$