We have the following function: 

$f(x) = \left\{ 
 \begin{array}{l l}
 x^2 \cos\left(\dfrac{1}{x}\right) & \quad \text{if $x \neq 0$}\\
 0 & \quad \text{if $x=0$}
 \end{array} \right.$

We want to show it's continuous everywhere. How does one do this? For $x=0$ I know you can use the squeeze theorem, but for all other points in the domain, how can you show that the function is continuous?