Question

I’m studying for an Algorithms exam and one of the practice problems is a little confusing to me. I’m supposed to prove logn is in Ω(log(logn)). I know of two ways to go about this: either using the definition of Ω (finding some constant C such that logn >= c * log(logn) for all c>=C), or using a limit comparison (take lim as n->inf of logn/log(logn) and show it equals infinity). My problem is that I don’t really know how to go about finding a constant for the first method, and for the second method I haven’t a clue as to how to evaluate that limit. Any tips? Thanks!

Answer 1

If you want to find the limit of a quotient f(x)/g(x) as x->infinity, where f(x) and
g(x) also go to infinity, the usual approach is to try applying L’Hôpital’s Rule
by taking the derivative of f(x) and g(x) and finding the limit of f'(x)/g'(x) as
x->infinity.