How do you know if a certain limit does not exist - without actually graphing it? What answer do you get that shows you there is no such limit?

  • $\begingroup$ What do you mean by "arithmetically"? How do you define the limit of a sequence/function? $\endgroup$ Nov 24, 2019 at 21:16
  • $\begingroup$ I mean not by drawing it out. $\endgroup$
    – Burt
    Nov 24, 2019 at 21:18
  • $\begingroup$ Usually I know it doesn't exist, because I proved it does not exist :) $\endgroup$ Nov 24, 2019 at 21:21
  • 1
    $\begingroup$ I would encourage you look over any of these existing questions about this topic: math.stackexchange.com/search?q=limit+not+exist $\endgroup$ Nov 24, 2019 at 21:22

1 Answer 1


This is rather broad, but in general:

  • In univariate calculus, if you can show that the limit from the left is not the same as the limit from the right, i.e. $\lim \limits_{x \to c^+} f(x) \ne \lim \limits_{x \to c^-}f(x)$, then it follows that the limit doesn't exist.
  • In multivariable calculus, you can do the same thing but showing different values of the limit for two different paths to a certain point.

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