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3. Determine and demonstrate the asymptotic complexity of the follow- ing function. Show your work and explain your reasoning. (Hint: Transform the function into a summation and use conventional bounding techniques.) (2 points] g(n) = log2(n!) 2 The Limit Theorem Recall that the Limit Theorem states that the following hold for asymptot ically positive functions f and g. lim f(n) 2-+00 g (n) 20 = 1f ( 1 ) Ew ( g ( n ) ) ] lim () = c0 = [f(n) co(g(n))] n-+0 g(n) lim f(n) n-40% g ( n ) 0 = 1/ (n) co(g (n ) ) ] The Limit Theorem is quite powerful, allowing us to analyse not just specific functions, but to compare entire classes of functions against each other. 5