Limit of (x³y)/(x⁵+2y³) as (x,y)→(0,0)

[oahsen]

how can I show that
lim of (x^3*y)/(x^5+2*y^3) when (x,y) goes to (0,0) is 0.
I tried to solve with epsilon-delta method and with sandwich method. however, all of my attempts resulted withous sucess? Which method should I use and how should ı start?

 

[Data]

The limit is not 0. It does not exist. Contrast the parameterizations y=x^2 and y=0.