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Definition 6.1.8: One-Sided Limits of a Function

If f is a function with domain D and c closure(D). Then:
  • f has a left-hand limit L at c if for every > 0 there exists > 0 such that if x D and c - < x < c then | f(x) - L | < . We write
    f(x) = L
  • f has a right-hand limit L at c if for every > 0 there exists > 0 such that if x D and c < x < c + then | f(x) - L | < . We write
    f(x) = L
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