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(a) Find the best possible relationship using one of the notations: O, , , o, , for the following pairs of functions: n 3 +

(a) Find the best possible relationship using one of the notations: O, , , o, , for the following pairs of functions: n 3 + 7n 1.5 3 and nlog8 10n0.5 + 7; nlgn and n 1.1 ; 5n and (5.1)n ; 4n and n!. Justify each answer.

(b) Function f(n) = n 3 + 5000n 60000 when n 50 and f(n) = nlog n + 100n for n > 50. Write f(n) in asymptotic notation in the simplest possible form.

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