Delta function

1. Dec 20, 2013

LagrangeEuler

1. The problem statement, all variables and given/known data
Show that
$\frac{1}{\pi}\lim_{\epsilon \to 0^+}\frac{\epsilon}{\epsilon^2+k^2}$
is representation of delta function.

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

3. 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?

2. Dec 20, 2013

Simon Bridge

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