(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to show that

[tex]\lim_{\epsilon\to 0}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}{\epsilon\over 2\pi [(x-x')^2+(y-y')^2+\epsilon^2]^{3\over2}}f(x,y)\;dx\,dy\,\,=f(x',y')[/tex]? I am not sure what conditions there is on [itex]f(x,y)[/itex], though I do know that [tex]\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}{z\over 2\pi [(x-x')^2+(y-y')^2+z^2]^{3\over2}}f(x,y)\;dx\,dy[/tex] is well-defined for all [itex]x,y\in R[/itex] and [itex]z>0[/itex].

2. Relevant equations

Please see above section.

3. The attempt at a solution

It is possible that we couldchange variables or sth? Or maybe show that in the limit, the green's function is the delta function? Please help!

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# Homework Help: Please help with finding the limit of the integral

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