1. Show directly that f(n) = n2 + 3n3 (n3). That is, use the definitions of O and Q to show that f(n) is in both O(n3) and (n3). Please use the formal definitions of Big-Oh, Theta, and Omega. You must show your work, clearly explain how you solved the problem. 2. Use mathematical induction to show that, for all integers n > 0, the following equation is true: (please show your work!) > k(k!) = (n + 1)! 1