I was asked the following question:

Find a function $f:\mathbb R^2 \to \mathbb R$ such that $f(x,y)$ has no limit as $x$ and $y$ approach zero, but $\lim\_{t\to 0} f(tv)=0$ for all $v \in \mathbb R^2$

I think I misunderstood the question. I mean, the fact that $f$ has no limit as $x,y$ approach zero, doesn't that mean that $\lim\_{t \to 0} f(tx,ty)$ doesn't exist?