For functions A and $B$ and constant $c>1,$ indicate which of

$(B),A=(B)$ holds. Here, we use the notation that $lo{g}_2=lg.$ Hint: for these

problems it is useful to know some mathematical identities. See CLRS section $3\mathrm{.}2$ or

CLRS Standard Notations and Common Functions in HuskyCT lecture notes.

$($a$)A=n^c,B=c^n$

$($b$)A=n^{lg(c)},B=c^{lg(n)}$

$($c$)A=lg(n!),B=lg(n^n).$ For this problem, you will find Stirling's approximation

useful: $n\sqrt[\phantom{2}]{2n}(\frac{n}{e}{)}^n(1+(\frac{1}{n})).$

$($d$)A=3^{3^n},B=3^{n^2}$