Two Variable Limit: Find/Prove Existence

[gateman234]

Homework Statement

Lim [x^2*y^3/(x^4 + y^4)]
(x,y)->(0,0)
Find the limit or prove it doesn't exist

Homework Equations

The Attempt at a Solution

Tried considering the limit along the line x=y, and y=x^2, but couldn't show there where different vaules of limit for different curves. Then i graphed it, and it looked like the limit exists.
Attempted proof.
|x^2 y^3/(x^4 + y^4) - 0| < E
0< sqrt(x^2 + y^2)< d
this is where I am stuck at.

 

[I like Serena]

A simple way is to set e.g. y=0 and then solve it with x->0.

More generally you'd like to move from a general direction to the origin, because sometimes it matters where you're coming from (not in this case).
You can do that by substituting (x,y) = lambda (a,b) where a and b are not both zero.
Then you take the limit for lambda->0.