Limits of $ f(x,y) = y\ (1-x)^{y-2} $ reach contradiction
Solution 1:
One can see that if $(x,y)$ tends to $(0,\infty)$ through the curve $y = 1/x^2$ the limit of $f(x,y)$ is $0$. On the other hand, if $(x,y)$ tends to $(0,\infty)$ through the curve $y = 1/x$ the limit of $f(x,y)$ is $\infty$.
This proves that $\displaystyle\lim_{x\to 0^+ \\ y\to\infty}f(x,y)$ doesn't exists.