# How do you know a limit does not exist?

In short, the limit does not exist if there is a lack of continuity in the neighbourhood about the value of interest.

Recall that there doesn't need to be continuity at the value of interest, just the neighbourhood is required.

A common misunderstanding is that limits DNE when there is a point discontinuity in rational functions. On the contrary, the limit exists perfectly at the point of discontinuity!

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A limit does not exist if the function approaches different values from the left and right sides of the point in consideration, or if the function approaches infinity or negative infinity. Additionally, if there are oscillations or fluctuations in the function as it approaches the point, the limit may also not exist.

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