Question: Please do ALL parts. Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2 (n)) (b) 2^n

Please do ALL parts. Please do ALL parts. Prove the following, using either the definition of

Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2 (n)) (b) 2^n elementof O(n!) (c) log_2 (n^2) + log_2 (100n^10) elementof O(log_2 (n)) d) n^1/2 middot O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n^2)

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