1. The problem statement, all variables and given/known data Given that: f(n) = n^(1.01) + n(log(n))^5 g(n) = n^(1.01) Show that: a) f(n) ∈ O(g(n)) b) f(n) ∈ Ω(g(n)) c) f(n) ∈ Θ(g(n)) 2. Relevant equations Any method as long as it's correct. It doesn't have to be strictly by using the definition of the big O notation but it could be using limits or any other correct method. 3. The attempt at a solution I can see how b is true. Also, given that I know the answer to a is true because the "solution" my teacher gave states it, I can automatically conclude that c is true because if both a and b are true, then c must also be true. I tried plugging in n = 1,000,000 and n(log(n))^5 grows larger than n^(1.01) which makes intuitive sense but seems to contradict a. Any help in showing that a is in fact true would be greatly appreciated! Thanks in advance!