Two multi-variable limit problems $$\lim_{(x,y)\to(0,0)}\frac{2x^2y}{x^4+3y^2}$$
I'm getting that the limit DNE because using $(0,y)\to(0,0)$ it is $0$ but for $(x,x^2)\to(0,0)$ it is $1/2$. Since $0$ does not equal $1/2$ the limit does not exist.
$$\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{2x^2+y^2}$$
I'm getting that the limit does not exist because using $(0,y)\to(0,0)$ it is $0$ but $(x,x^2)\to(0,0)$ it is $1$. Since $1$ does not equal $1$ the limit does not exist.
Can someone check my answers and tell me if my reasoning is correct?
Thanks!

Yeah, you're right, from showing that you can say that the limit does not exists, from more you can say this in terms of the formal definition of a limit, but, with this approach it's enought to say that the limit does not exists
