m 1. Show directly that f(n) = n2 + 3n3 = O(n3). That is, use the...

 

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m 1. Show directly that f(n) = n2 + 3n3 = O(n3). That is, use the definitions of O and to show that f(n) is in both O(n3) and Q(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!) n - k (k!) = (n+1)! 1 k=1 m 1. Show directly that f(n) = n2 + 3n3 = O(n3). That is, use the definitions of O and to show that f(n) is in both O(n3) and Q(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!) n - k (k!) = (n+1)! 1 k=1