Multivariable Calculus: When to use Squeeze Theorem to solve limits?

[theBEAST]

Homework Statement

For example in:
lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)]

This limit does not exist (according to textbook), but if you use squeeze theorem since y^2<(x^2+y^4)
y^2/(x^2+y^4) <= 1 and therefore

0 <= (xy^2)/(x^2+y^4) <= x
as x--> 0
so
lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)] = 0?

 

[dirk_mec1]

What happens if you look at y=sqrt(x)?

 

[theBEAST]

What happens if you look at y=sqrt(x)?

I see what you mean but what if i was looking at a different limit and I got 0 every time while using different paths. I still couldn't prove it with squeeze theorem because what if there is just this one path that i never tried.