Prove that $\lim_{(x,y)\to(0,0)} {xy\over x^2-2y}$ does not exists

Question

I've got a problem in proving the fact, that limit of function does not exists.
Any ideas? It would be great.
Thanks

$\lim_{(x,y)\to(0,0)} {xy\over x^2-2y}$

Answer 1

HINT

Let consider for $t\to 0$

• $x=t \quad y=t$
• $x=t\quad y=\frac{t^2}2+t^3$