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To check for the existence of a limit of a function at a point, you can use the following conditions:
The function must be defined in a punctured neighborhood of the point.
The limit of the function as it approaches the point must exist and be finite.
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.
Chip Romig, MMR 423
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