3-2 Relative asymptotic growths

Indicate, for each pair of expressions $(A, B)$ in the table below whether A is $O, o,\Omega,\omega$, or $\Theta$ of B. Assume that $k \geq 1,\epsilon >,$ and $c>1$ are constants. Write your answer in the foem of the table with "yes" or "no" written in each box.

A	B	O	o	$\Omega$	$\omega$	$\Theta$
$\lg^k n$	$n^{\epsilon}$	yes	yes	no	no	no
$n^k$	$c^n$	yes	yes	no	no	no
$\sqrt{n}$	$c^{\sin n}$	no	no	no	no	no
$2^n$	$2^{n/2}$	no	no	yes	yes	no
$n^{\lg c}$	$c^{\lg n}$	yes	no	yes	no	yes
$\lg (n!)$	$\lg (n^n)$	yes	no	yes	no	yes