Why is the multi-variable function $f(x,y)=\exp(-1/(x^2+y^2))$ continuous? I don't understand this problem:

Show that the function $f: \mathbb R^2\to \mathbb R$ given by $$f(x,y)=\exp\left\{\frac{-1}{x^2+y^2}\right\}$$ for $(x,y)≠(0,0)$ and  $f(0,0)=0$ is continuous at $(0,0)$.    


hint:use the inequality: $e^{-u} \leq \dfrac{1}{1+u}$ with $u = \dfrac{1}{x^2+y^2}$.
