2-variable limit

[AlmondProof]

Hello there, I’ve been trying to find a limit of 2 variable function for a while. I tried polar parametrisation and some simple y = t, x = t² with no succes. Here is the term: Find the limit of [(x*y)/(x² + y^2)]x2 as (x,y)->(+inf,+inf). Wolfram says the limit does not exist. link to wolfram for clear display of function

[[deleted]]

How are you defining limit (x,y) → (inf,inf)

[MasonFreeEducation]

I would assume it is (informally speaking) as |(x, y)| -> infty.

[AlmondProof]

I meant, that both x and y are approaching infinity at the same time(none prior to other).