[Q1] Prove that n^3 3n^2 n+1 = (n^3). [Q2] Prove or disprove: (n^2) = (n^2 + 1). [Q3] Suppose you have algorithms with the six running times listed below. (Assume these are the exact number of operations performed as a function of the input size n.) Suppose you have a computer that can perform 1010 operations per second. For each algorithm, what is the largest input size n that you can complete within an hour? (a) n^2 (b) n^3 (c) 100n^2 (d) nlogn (e) 2n (f) 22n