(Solved): (8 pts) This question tests your understanding of proofs for asymptotic notat ...

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(8 pts) This question tests your understanding of proofs for asymptotic notations. (a) Let $$f(n)=3n^2?1000$$. In order to prove that $$f(n)??\left(n^2\right)$$, we need to find a positive constant $$c>0$$ and an integer $$N?1$$ such that $$f(n)?c\times n^2\text{, for every }n?N.$$ 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 $$g(n)=13n^2+1000$$. In order to prove that $$g(n)?O\left(n^2\right)$$, we need to find a positive constant $$c>0$$ and an integer $$N?1$$ such that $$g(n)?c\times n^2\text{, for every }n?N.$$ 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): $$c=14,N=10$$