Finding The Limit Of A 3D Function

[Baumer8993]

Homework Statement

Find the limit as X, and Y both approach 0 of (X²Y)/(X² + Y⁴)

Homework Equations

The equation from above.

The Attempt at a Solution

I have been doing the technique of approaching from different lines such as y = x, or x = y,
x = 0, and y = 0. All of them give me a limit of zero, so that will not do. I graphed the function online, and it appears as if the function does have a limit of zero. How would I prove this? I think I need to do something with polar coordinates, but I am not sure how to do that.

 

[BloodyFrozen]

EDIT:
I'd go with SammyS's

 

[SammyS]

Homework Statement

Find the limit as X, and Y both approach 0 of (X²Y)/(X² + Y⁴)

Homework Equations

The equation from above.

The Attempt at a Solution

I have been doing the technique of approaching from different lines such as y = x, or x = y,
x = 0, and y = 0. All of them give me a limit of zero, so that will not do. I graphed the function online, and it appears as if the function does have a limit of zero. How would I prove this? I think I need to do something with polar coordinates, but I am not sure how to do that.

Yes. Change to polar coordinates.

$x=r\cos(\theta)$

$y=r\sin(\theta)$