$($a$)(9$ points$)$ Use the Master Theorem to solve the following recurrence:

$T(n)=2T(\frac{n}{2})+n^2.$

$($b$)(16$ points$)$ Using the recurrence you found in part a$,$ answer the following yes$/$no ques$-$

tions. Circle your answer.

Is $T(n)=O(logn)?$

Is $T(n)=(logn)?$

Is $T(n)=O(n)?$

Is $T(n)=(n)?$

Is $T(n)=O(n^2)?$

Is $T(n)=(n^2)?$

Is $T(n)=O(n!)?$

Is $T(n)=(n!)?$