With the limit definition of the big oh, you are doing a limit at infinity, and the formula looks like

lim->infinity g(n)/f(n)

there are three possible outcomes here, you get infinity, 0 or a nonzero constant as a final answer. I have a book that shows this, but uses little oh to show what each answer represents, can someone explain what the answers mean in terms of big oh?

Example:

Show 3n^5 + 4n^4 +3n + 3 belongs to theta of (n^5)

Spoiler

I believe the final answer is 1/3 if im not mistaken, does it mean that it IS in theta of n^5?

also, what would it mean if I got zero as an answer, how about if I got infinity?

Thanks!