MathAnalysisCalculusLimits

One-sided limits and the non-existence of a limit

Theory

One-sided limits

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Suppose there exist one-sided limits lim⁡x→a+f(x)=A\lim\limits_{x\to a+} f(x) = A and lim⁡x→a−f(x)=B\lim\limits_{x\to a-} f(x) = B. Does the limit lim⁡x→af(x)\lim\limits_{x\to a} f(x) exist?

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