Asked by Marcus
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.
I'm not even too sure what this means in calculus terms. Can you please explain it better? Thank you.
Answers
Answered by
Steve
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.
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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