(8 pts) This question tests your understanding of proofs for asymptotic notations. (a) Let f(n)=3n21000. In order to prove that f(n)(n2), we need to find a positive constant c>0 and an integer N1 such that f(n)cn2,foreverynN. Answer the following questions on the answer sheet. (a1) Will c=1,N=8 make the proof correct? (a2) Will c=3,N=12 make the proof correct? (a3) Will c=5,N=13 make the proof correct? (a4) Will c=7,N=20 make the proof correct? (b) Let g(n)=13n2+1000. In order to prove that g(n)O(n2), we need to find a positive constant c>0 and an integer N1 such that g(n)cn2,foreverynN. Answer the following questions on the answer sheet. (b1) Will c=11,N=32 make the proof correct? (b2) Will c=12,N=20 make the proof correct? (b3) Will c=13,N=20 make the proof correct? (b4) Will c=14,N=10 make the proof correct? Q4: Read the instructions for question Q4 in the assignment document. For each of the 8 sub-questions check the box if and only if whose corresponding values for c and N make the proof correct. (a1): c=1,N=8 (a2): c=3,N=12 (a3): c=5,N=13 (a4): c=7,N=20 (b1): c=11,N=32 (b2): c=12,N=20 (b3): c=13,N=20 (b4): c=14,N=10