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For this homework, use the following conventions Definition of Natural Numbers: the set of natural numbers is the set of non-negative integers, denoted N. That is N={0, 1, 2, 3, ) When discussing asymptotic analysis of functions, we will restrict our attention to non-negative, non-decreasing functions with domain N. That is, if fis such a function, then (non-negativity) f (n) 20 for all n o (non-decreasing) If n 0 g(n) Problems 1. Let f (n) = 3n2 + 2n + 4. Use the definition of Big-O to prove that f (n) = O (n2) 2. Use the Big-O limit Lemma to show that log(n) - O (n). Then use the limit lemma to show that n* logn - 0 (n+) for any constant 3. Let a and b be any constants equal to or larger than 2 such that a