The limit theorem for asymptotic analysis tells us that if we have two functions f(x) and g(x), such that limx!1 f(x)/g(x) = c, for some finite c, then f(x) = O(g(x)). Is the opposite true? That is, if f(x) = O(g(x)), must it be the case that limx!1 f(x)/g(x) = c, for some finite c?