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

. 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 for every sequence an −→ u with an ∈ (a, b), we have that lim f(an) = L ∈ R. Prove that lim x−→u f(x) = L.

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