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Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite...

Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite open interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a function and that lim x−→u f(x) = L ∈ R. Prove that for every sequence an −→ u with an ∈ (a, b), we have t

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