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For each of the following pairs of functions f and g (both of which map the...

For each of the following pairs of functions f and g (both of which map the naturals N to the reals R), state whether f is O(g), Ω(g), Θ(g) or “none of the above.” Prove your answer is correct. 1. f(x) = 2 √ log n and g(x) = √ n. 2. f(x) = cos(x) and g(x) = tan(x), where x is in degrees. 3. f(x) = log(x!) and g(x) = x log x.

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