Question: Let I be an open interval containing 0, and let f, g : I R . Assume that limx0 f(x) g(x) = 1, and limx0

Let I be an open interval containing 0, and let f, g : I R . Assume that limx0 f(x) g(x) = 1, and limx0 g(x) = L > 0. Prove that there exists > 0 such that for all x I such that 0 < |x| < , it holds that |f(x) g(x)| < 1.

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