# Prove the property of Dirac's Delta

1. Apr 11, 2012

### phy07

Last edited by a moderator: May 5, 2017
2. Apr 12, 2012

### clamtrox

Let $$\lbrace x_i \rbrace$$be the zeroes of function f(x). Near the zeroes, you can write the function as $$f(x) = f'(x_i)(x-x_i) + O(x-x_i)^2.$$ As the Dirac delta is entirely localized at xi, you can just drop all higher order terms and it's still exact. Then you can use the scaling property of delta function, http://en.wikipedia.org/wiki/Dirac_delta_function#Scaling_and_symmetry

3. Apr 12, 2012

### phy07

Ok. Thank you clamtrox.

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