Find the limit: $\lim\limits_{(x,y)\to (0,0)}\frac{x^3 - y^3}{x^2+y^2}$ We seek a solution to the limit question: $$\lim\limits_{(x,y)\to (0,0)}\frac{x^3 - y^3}{x^2+y^2}$$
I have an approach and think I have an answer but wanted to ask the community first. My approach is similar to the approach BabyDragon used at this link: What is $\lim_{(x,y)\to(0,0)} (x^3+y^3)/(x^2-y^2)$?

We have
$$0\le\left|\frac{x^3-y^3}{x^2+y^2}\right|\le \frac{|x|x^2+|y|y^2}{x^2+y^2}\le|x|+|y|\to0$$
so the desired limit is $0$
