Let fn log n Let gn cube root of n Select the first answer

Let f(n) = log n Let g(n) = cube root of n Select the first answer below that is true. f is Theta (g) f is Theta (g) f is Ohm (g)

Solution

Case 1: f(n) = (nc), where c < logb a

Case 2: f(n) = (nc logk n), where c = logb a

Case 3: f(n) = (nc), where c > logb a

Now there is no direct dependence on the choice of n anymore - all that matters is the long-term growth rate of f and how it relates to the constants a and b. Without seeing more specifics of the particular recurrence you\'re trying to solve, I can\'t offer any more specific advice.