I don't have an equation for this. I'm looking more for intuition rather than anything else. At what point in the epsilon-delta definition of a limit does this fail to hold up?
I'm having trouble understanding the epsilon-delta definition of a limit and why it's defined the way it is.
Best Answer
Call the size of the jump $a$. Choose $\varepsilon=a/2$. Then no matter how small you choose $\delta$, there will be $x$ (on the other side of the jump from $x_0$) such that $|x-x_0|<\delta$ and $|f(x)-f(x_0)|>\varepsilon$.