What does it mean to say that f(3) exists but that there is no limit to f(x) as x approaches 3?

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- Feb 26th 2010, 02:57 PMsatxFunctions without limits
What does it mean to say that f(3) exists but that there is no limit to f(x) as x approaches 3?

- Feb 26th 2010, 03:08 PMRandom Variable
It means that the limit is dependent upon the path you take.

- Feb 26th 2010, 03:11 PMDrexel28
- Feb 26th 2010, 03:15 PMsatx
- Feb 26th 2010, 03:18 PMDrexel28
- Feb 26th 2010, 03:22 PMsatx
- Feb 26th 2010, 03:26 PMPlato
- Feb 26th 2010, 03:27 PMRandom Variable
- Feb 26th 2010, 03:28 PMRandom Variable
What about a function that oscillates wildly near a point?

- Feb 26th 2010, 03:31 PMDrexel28
- Feb 26th 2010, 03:43 PMRandom Variable
Does that count? (Giggle)

If I remember correctly, in real analysis we proved that $\displaystyle \lim_{x \to 0} \sin(1/x) $ does not exist by finding a sequence $\displaystyle (s_n)$ that converges to some value c ($\displaystyle s_{n} \ne c$) but where $\displaystyle f(s_n)$ doesn't converge (or something like that). - Feb 26th 2010, 03:52 PMDrexel28