Question: (12 pts) Consider the function f(n) = n2 + 1000n, and do the following: a) Prove that f(n) = O(ny) by finding a co and

(12 pts) Consider the function f(n) = n2 + 1000n, and

(12 pts) Consider the function f(n) = n2 + 1000n, and do the following: a) Prove that f(n) = O(ny) by finding a co and no such that f(n) no. b) Prove that f(n) = O(na) by finding a ci and n such that f(n) ni. c) Prove that f(n) = N2(na) by finding a c2 and n2 such that f(n) > 02:n2 for n >n2. d) Prove that f(n) = O(n) by finding a C3, Cz, and nz such that c3.n2 = f(n) n3

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