Epsilon Delta Proof of a Limit

The problem is give a rigerous epsilon delta proof that lim (x,y) ⟶ (0,0) (x^3 + y^3)/(x^2 + y^2)

Heres what I have. Given any ε > 0, we can find a corresponding δ > 0 such that if 0 < || (x,y) - (0,0)|| < δ , then (x^3 + y^3)/(x^2 + y^2) < ε

0 < √(x^2 +y^2) < δ

√(x^2) =|x|< δ
√(y^2) = |y| < δ

I'm stuck after this part. Is the above part even correct? If so, how do I finish i then?

Thanks

Quote:

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Originally Posted by meks08999

The problem is give a rigerous epsilon delta proof that lim (x,y) ⟶ (0,0) (x^3 + y^3)/(x^2 + y^2)

Heres what I have. Given any ε > 0, we can find a corresponding δ > 0 such that if 0 < || (x,y) - (0,0)|| < δ , then (x^3 + y^3)/(x^2 + y^2) < ε

0 < √(x^2 +y^2) < δ

√(x^2) =|x|< δ
√(y^2) = |y| < δ

I'm stuck after this part. Is the above part even correct? If so, how do I finish i then?

Thanks

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so we need to choose

Thanks for the help.