How would you prove this generalization about the connection between two-sided and one-sided limits?

Prove that in order for the normal, two-sided limit to exist,
the one-sided limits (approaching from left and right) have to both exist and be equal?

Please explain step-by-step. Thanks.

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One Response to “How would you prove this generalization about the connection between two-sided and one-sided limits?”

  1. ben e said:

    It would be easier to show that if either one-sided limit doesn’t exist, the the two-sided limit doesn’t exist and if the one-sided limits aren’t equal, then the the two-sided limit doesn’t exist.




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