Let $\displaystyle \lim := \lim_{x \to a}$. Suppose $\displaystyle \lim f/g$ exists. Under what conditions can we say $\displaystyle \lim {f+o(1) \over g+o(1)}$ exists and is equal to $\displaystyle \lim f/g$? (Little o's are as $\displaystyle x\to a$.)