Prove the property of Dirac's Delta

[phy07]

Homework Statement

How can i prove this property of Delta,
http://e1204.hizliresim.com/w/d/4bw2j.png

Homework Equations

This is my homework from John David Jackson's Classical Elektrodynamics book

The Attempt at a Solution

I can't an attempt. Some properties is proved at wiki and other web pages but didn't find this.

(http://en.wikipedia.org/wiki/Dirac_delta_function and ... )

 

[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 x_i, 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

 

[phy07]

Ok. Thank you clamtrox.