Question $3$

Prove or disprove the following statements, using the relationship among typical growth$-$rate

functions seen in class.

a$)n^{22}logn+n^7$ is $(n^{6}logn)$

b$){10}^7{n}^5+5n^4+9000000n^2+n$ is $(n^7)$

c$)n!$ is $(n^n)$

d$)0\mathrm{.}01n^8+800000n^6$ is $(n^8)$

e$)n^9+8000n^7$ is $(n^{16})$

f$)n!$ is $O(4^n)$