For each function $f(n)$:$Z^{+}{R}^{+}$give the value of smallest nonnegative integer $k$ such that $f(n)inO(n^k).$ In other words, give the value

of $k$ such that $O(n^k)$ is the most restrictive polynomial$-$time upper bound of $f(n).$ If no such bound exists, type $8$ e$99$ in the space

provided.

A$)3n^2+\frac{1}{n}$inO$(n^k),k=$

B$)17\sqrt[3]{n+4}+5\sqrt[\phantom{2}]{7n}+4in0(n^k),k=$

C$)2^{lgn}+1000000$inO$(n^k),k=$

D$)3^{2n+1}$inO$(n^k)k=$

E$)5n^{2}lg\sqrt[\phantom{2}]{n^3+4n+7}$inO$(n^k),k=$