Question: 3. (10 points) Answer the following by using the definitions for asymptotic notations: a) Prove that 10Vn - O(n) b) Is 2n-(2)? Either prove or

3. (10 points) Answer the following by using the definitions for

3. (10 points) Answer the following by using the definitions for asymptotic notations: a) Prove that 10Vn - O(n) b) Is 2n-(2)? Either prove or explain your answer. 4. (8 points) A program takes 10 seconds for input size 1e0e (i.e., n-1000) Ignoring the effect of constants, approximately how much time can the same program be expected to take if the input size is increased to 2000, under each of the following run-time complexities? a) O(N) b) O(N logN) c) O(N)

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