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 $\lim_{(x,y)\to(0,0)} (x^3+y^3)/(x^2-y^2)$?

What about using some polar coordinates?
$$x=r\cos t\;,\;\;y=r\sin t\implies\begin{cases} x^3-y^3=r^3(\cos t-\sin t)\left(1+\frac12\sin2t\right)\\{}\\(x,y)\to(0,0)\iff r\to 0\end{cases}$$
$$\frac{x^3-y^3}{x^2+y^2}=\frac{r^3\left(\cos^3t-\sin^3t\right)}{r^2}=r(\cos t-\sin t)\left(1+\frac12\sin2t\right)\xrightarrow[r\to 0]{}0$$
