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For each of the following two functions f(n) and g(n), indicate whether f = O(g), or f = Ω(g) or both (in which case f = Θ(g)).

(a) f(n) = √ n and g(n) = n/∛n.
(b) f(n) = 100n + lg n and g(n) = n + (lg n)².
(c) f(n) = 10n lg n and g(n) = n lg (10n).
(d) f(n) = 10 lg n and g(n) = lg (n²).
(e) f(n) = n²/ lg n and g(n) = n(lg n)².
(f) f(n) = n2ⁿ and g(n) = 3n.
(g) f(n) = 2ⁿ and g(n) = 2ⁿ⁺¹⁰⁰.

Sagot :

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