Is $1/(x^2 + y^2)$ continuous?

I'm trying to check whether the function $$ f(x,y)=\begin{cases} \dfrac{1}{x^2+y^2} & \text{for $(x,y)\ne(0,0)$}\\[6px] 0 & \text{for $(x,y)=(0,0)$} \end{cases} $$ is continuous. My problem is with trying to check if $$ \lim_{(x,y)\rightarrow(0,0)}\frac{1}{x^2+y^2} = 0, $$ Any clues on how to do it?

The function is clearly continuous everywhere, except at $(0,0)$.

To see why it's not continuous at $(0,0)$, consider the restriction of the function to a line through the origin, for instance $y=0$. Since $$ \lim_{x\to0}f(x,0)=\lim_{x\to0}\frac{1}{x^2}=\infty $$ you have the answer.