# Limit involving dirac delta distributions

1. Feb 26, 2012

### thrillhouse86

Hey All,

I am trying to evaluate the limit:
$$\lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)}$$

Where $$\delta'(x)$$ is the first derivative of the dirac distribution and $$\delta''(x)$$ is the second derivative of the dirac distribution.

I thought about the fact that this expression will be infinity / infinity and then using L'Hospitals but that doesn't help.

I guess my question (as someone with an engineering / physics background and not a mathematician) is this limit impossible to evaulate ? and if so is it impossible because taking the limiting value of a dirac distribution doesn't make a whole lot of sense ?

Thanks

2. Feb 27, 2012

### thrillhouse86

Sorry I mean to evaulate:
$$\lim_{x\to 0^{+}} \frac{\delta'(x)}{\delta''(x)}$$

3. Feb 27, 2012

### M Quack

Try writing the delta function as limit of a Gaussian, for example.

4. Feb 27, 2012

### Hurkyl

Staff Emeritus
Where did this limit come from? I don't believe it even makes sense....