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I NEED THE ANSWERS FOR QUESTIONS 8 and 9 PLEASE SHOW WORK 8. Use mathematical induction to show that when n is an exact power

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I NEED THE ANSWERS FOR QUESTIONS 8 and 9
PLEASE SHOW WORK
8. Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence T(n) = [2 12r 2T (n2)+n ifn 2k, for k> is T (n) -nlg n. (10 points) sort algorith 9. Prove the following theorem. the worst case." (10 points) "Any comparison sort algorithm requires (n lg n) comparisons in

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