f=x y^2/(x^2+y^4)

Plot3D[f,{x,-3,3},{y,-3,3}]
ContourPlot[f,{x,-3,3},{y,-3,3}]

g=f/.{x->t^2,y->t}

h=f/.{x->t,y->3t}

Limit[h,t->0]