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A function can be continuous at every point of a deleted neighborhood of some point and still not have a limit at the point which is deleted.

I'm not even too sure what this means in calculus terms. Can you please explain it better? Thank you.

1 answer

Consider f(x) = 1/x
f is continuous at every point in every neighborhood not including x=0.
Yet f does not have a limit at x=0; in fact it is not even defined at x=0.
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