Part B:

For each running time below, find positive constants $c$ and $n_0($or $c_1,c_2,$ and $n_0$ if necessary$)$ to

prove that $f(n)\text{'}$s running time is in Big $O(O),$ Big Omega $()$ or Theta $()$ of $g(n).$ Don't choose

wildly random values for $c($or $c_1$ and $c_2)$ and $n_0.$ Circle$/$box$/$highlight your answers! Show your

work for partial credit.

Show that $6n^2+3n+10$ is $O(n^2)$

Show that $6n^2+3n+10$ is $(n^2)$

Show that $2n$ is $(n)$

Show that $\frac{5n^2-n+2}{2}$ is $(n^2)$ for all $n{n}_0,$ where $n_0=1$

Show that $5$ is $(1)$

Show that $3n(lg(4n))$ is

Part B:

For each running time below, find positive constants $c$ and $n_0($or $c_1,c_2,$ and $n_0$ if necessary$)$ to

prove that $f(n)\text{'}$s running time is in Big O$($O$),$ Big Omega $()$ or Theta $()$ of $g(n).$ Don't choose

wildly random values for c $($or $c_1$ and $c_2)$ and $n_0.$ Circle$/$box$/$highlight your answers! Show your

work for partial credit.

$12$ points for question $6,10$ points for each other question

Show that $6n^2+3n+10$ is $O(n^2)$

Show that $lg(n)+1$ is