Showing the Representation of the Delta Function

[LagrangeEuler]

Homework Statement

Show that
$\frac{1}{\pi}\lim_{\epsilon \to 0^+}\frac{\epsilon}{\epsilon^2+k^2}$
is representation of delta function.

Homework Equations

$\delta(x)=\frac{1}{2 \pi}\int^{\infty}_{-\infty}dke^{ikx}$

The Attempt at a Solution

$\int^{\infty}_{-\infty}\frac{\epsilon}{\epsilon^2+k^2}dk=\pi$
One can take $F[e^{-\epsilon x}]$ and then put $\epsilon to go to zero +. Why$0^+##. I'm confused?

 

[Simon Bridge]

Why $0^+$. I'm confused?

What happens when you take the limit from the other side?