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Let A ? R, let f : A ? R be a function, and let...

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Advance Math

Let A ? R, let f : A ? R be a function, and let c be a limitpoint of A. Suppose that a student copied down the followingdefinition of the limit of f at c: “we say that limx?c f(x) = Lprovided that, for all ? > 0, there exists a ? ? 0 such that if0 < |x ? c| < ? and x ? A, then |f(x) ? L| < ?”. What wasthe student’s mistake? If this were the correct definition of alimit, which functions would have which limits, and at whichpoints?

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