How to prove $\lim_{(x,y)\to(0,0)}\frac{x^2y}{3x^2+0.5(x-1)^2y^2}$ doesn't exist? Initially I thought the limit was 0, but when I checked in Wolfram Alpha's calculator, I got that the limit doesn't exist. 
Why is this the case? I couldn't find a trajectory for which the limit doesn't exist, so how am I supposed to find out it doesn't have a limit? Can I prove its non-existence using the epsilon-delta definition?

we have
$|f(x,y)|<\frac{|y|}{3}$
so , $\lim_{(x,y)\rightarrow (0,0)}f(x,y)=0$.
