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10 Nov 2019

3. Prove or disprove (formally) the following:

(a) n log2 n â O(2n 1/3 ).

(b) log(5n) â O(log(2n)).

(c) 2 2 n+1 â O(22 n ).

(d) [f1(n) â O(g1(n)) â§ f2(n) â O(g2(n))] ââ [f1(n) + f2(n) â O(g1(n) + g2(n))].

3. Prove or disprove (formally) the following: (a) nlog?n Ñ 0(2n1/3). (b) log(5") O(log(2")) (c) 22n+1 EO(22n) log n

3. Prove or disprove (formally) the following:

(a) n log2 n â O(2n 1/3 ).

(b) log(5n) â O(log(2n)).

(c) 2 2 n+1 â O(22 n ).

(d) [f1(n) â O(g1(n)) â§ f2(n) â O(g2(n))] ââ [f1(n) + f2(n) â O(g1(n) + g2(n))].

3. Prove or disprove (formally) the following: (a) nlog?n Ñ 0(2n1/3). (b) log(5") O(log(2")) (c) 22n+1 EO(22n) log n

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Jarrod RobelLv2

5 Nov 2019