Function f(x) such that it's continuous

[emyt]

LaTeX Code: \\lim_{x\\to a} f(x)= L
It means that the value of x reaches a, the value of f(x) also reaches L.

this is more like:

AS x APPROACHES a, f(x) APPROACHES L. If x reaches a, then f(x) is just f(a), but I'm pretty sure you have the idea, f(x) may not be able to reach f(a) - then the limit of that "approach" is L.

 

[dE_logics]

The distance form f(x) to L, f(x)- L (not f(x) alone), can be larger than $\epsilon$ for some x, just not for x "sufficiently close" to a. Once x is within some distance of a, |f(x)- L| cannot exceed $\epsilon$. And that "distance" is, of course, $\delta$.

Yes, I was expecting this barrier...thanks for telling.

Close but not exactly. The value f(x) "reaches" when x reaches a is f(a). The question is what happens when x is close to a but not equal to a.

Yes, I'll modify that sentence accordingly.

It should be close.

Ok then, thanks everyone!