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Answer to Question #48596 in Real Analysis for era

Question #48596
Suppose that f is defined on a deleted neighborhood of x0. Denote by
D(f) the domain of f. Show that the following statements are equivalent:

a) lim x -> x0 = L

b) whenever {uk} is a sequence in D(f) \ {x0} that converges to x0, then the sequence {f(uk)} converges to L
0
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