Show that the function
$$f(x,y)=\exp\left(\frac{1}{r^2-1}\right), if \;r<1$$ $$f(x,y)=0, if \; r \geq 1$$
Where $r =||(x,y)||$ is continuous in $R^2$
If $r>1$ or $r<1$ it is clearly continuous. But I need to analyze when $r \to 1:$ It looks like a transformation for polar coordinates, but I can't find the equivalent limit in $ R^2$ when $r \to 1.$ What should I do?
Thanks!