This question tests your understanding of proofs for asymptotic notations. (a) Let f(n) = 5n2 +10000. In order to prove that f(n) 2 O(n2), we need to nd a positive constant c > 0 and an integer N 1 such that f(n) c n2; for every n N: (1) Answer the following questions on the answer sheet. (a1) Will c = 6;N = 100 make the proof correct? (a2) Will c = 6;N = 200 make the proof correct? (a3) Will c = 7;N = 100 make the proof correct? (a4) Will c = 6;N = 50 make the proof correct? (a5) Will c = 5;N = 100 make the proof correct? (b) Let g(n) = 5n2 10000. In order to prove that g(n) 2 (n2), we need to nd a positive constant c > 0 and an integer N 1 such that g(n) c n2; for every n N: (2) Answer the