Prove or disprove the following statements, using the relationship among typical growth-rate functions seen in class.

a)n^15log n + n^9 is O(n^9 log n)

b) 15^7n^5 + 5n^4 + 8000000n^2 + n is (n^3)

c) n^n is (n!)

d) 0.01n^9 + 800000n^7 is O(n^9)

e) n^14 + 0.0000001n^5 is (n^13)

f) n! is O(3n)