# Epsilon-Delta proof help

1. Aug 26, 2009

### rman144

I need to show that:

$\lim_{x \to 0} x^{2}sin(1/x)=0$

Using the epsilon-delta method. I figured delta=sqrt[epsilon] would make the limit hold, but wanted to be sure. Thanks in advance.

2. Aug 26, 2009

### ╔(σ_σ)╝

I believe it can be show that if $$\epsilon$$ = $$\delta$$

$abs(x^{2}sin(1/x))\leq x^{2}$ < $$\epsilon$$

3. Aug 26, 2009

### Liwuinan

$$\delta = \sqrt{\varepsilon}$$ is ok too, |sin(...)| will be always less or equal to 1, so $$\varepsilon \left|\sin(1/\sqrt{\varepsilon})\right| \leq \varepsilon$$

4. Aug 26, 2009

### ╔(σ_σ)╝

This is more sufficient.:)