I am working on this practice question for an upcoming exam.
I am not sure if I am oversimplifying this here (as the question is worth 3 marks):
In polar coordinates I have:
$\ln(\sin(r^2))$, so on any path, as $(x,y)\rightarrow(0,0)$, $r\rightarrow 0$.
For $r$ sufficiently close to 0, lim $r\rightarrow 0$ r$\sin(r^2) = 0$. Therefore, $\ln(\sin(r^2))\rightarrow -\infty$.
We are allowed to take $-\infty$ as a a valid limit.
Any help/hints would be greatly appreciated!