Is $\frac{x^2y^2}{\sqrt{x^2+y^2}}$ continuous? Let $f: \mathbb{R}^2 $ -> $\mathbb{R}$
I was wondering if this function is a continuous function. 

Can I just say that $\frac{x^2y^2}{\sqrt{x^2+y^2}}$ is continuous everywhere except perhaps at $x=0$, because $\lim_{x\rightarrow \infty}$ $\frac{x^2y^2}{\sqrt{x^2+y^2}}$ = $\infty$, and the definition is that if $\lim_{x\rightarrow c}$ $f(x)$ = $f(c)$ then $f(x)$ is continuous at $c$. 

Let $|x| <1$, $|y|<1$.
$|f(x,y)| =|\dfrac{x^2y^2}{\sqrt{x^2+y^2}} | \lt$
$\dfrac{|x||y|}{\sqrt{x^2+y^2}} =$
$\dfrac{\sqrt{x^2}\sqrt{y^2}}{\sqrt{x^2+y^2}}\le$
$\dfrac{\sqrt{x^2+y^2}\sqrt{x^2+y^2}}{\sqrt{x^2+y^2}}=$
$\sqrt{x^2+y^2} .$
Choose $\delta = \epsilon.$
