F(x,y)=(x^2 y)/(x^4 + y^2). Show that lim (x,y)->(0,0) does not exist.?

HINT: compute limit along the parabola y=x^2...

idk how this works plesae help

Along the parabola y = x^2 we have

F(x,y) = x^2*x^2 / (x^4 + (x^2)^2) = x^4 / (2*x^4) = 1/2.

Now along the y-axis we have x = 0 and so F(x,y) = 0.

So along one curve we have F(x,y) -> 1/2 as (x,y) -> (0,0),

and along another we have F(x,y) -> 0 as (x,y) -> (0,0).

Since these two values are not equal, we conclude that the

lim((x,y) -> (0,0))(F(x,y)) does not exist.

let x =0, y =0
then F(x,y) = (0^0) / (0^4+0^2) = 1/0
because the denominator is 0 therefore the answer is undefined.

So lim (x,y) --> (0,0) doesn't exist.