Request for example of function to apply two path test with elliptic spirals

Question

I'm writing a quiz for my multivariable calculus class, and I'm trying to come up with a function $f:D\subseteq\mathbb{R}^2\setminus\{ 0\}\to\mathbb{R}$ such that (1) $\displaystyle\lim_{(x,y)\to(0,0)} f(x,y)$ doesn't exist and (2) we can show that limit doesn't exist by considering two different elliptical spirals ${\bf r}_{a,b}(t)=\langle at\cos(t),bt\sin(t)\rangle$.

Does anyone here happen to know of such an example?

Thank you for reading this, and if you reply, thanks in advance!