I have to prove that a function in little o composed with a function in big O is still in little o. I'm not sure if I'm on the right track here. For ease of notation, I'll denote f as the little o function and g as the big O function Clearly,
f(g(0)) = f(0) = 0, so that satisfies the first part of the little o definition. Here's where things get tricky because I kind of suck at function ...