multivariable limit of $\frac{x^2-y^2}{\sqrt{x^2+y^2}}$ Calculate multivariable limit of $$\lim_{(x,y) \rightarrow (0,0)}\frac{x^2-y^2}{\sqrt{x^2+y^2}}$$
How to do that? I was trying to figure out any transformations e.g. multiplying by denominator but I do not think it gives me any solution.

$$\lim_{(x,y) \rightarrow (0,0)}\frac{x^2-y^2}{\sqrt{x^2+y^2}}$$
Transforming $x=r\cos\theta, y=r\sin\theta$.
 $$\lim_{(x,y) \rightarrow (0,0)}\frac{x^2-y^2}{\sqrt{x^2+y^2}}=\lim_{r \rightarrow 0}\frac{r^2\cos^2\theta-r^2\sin^2\theta}{\sqrt{r^2\cos^2\theta+r^2\sin^2\theta}}=\lim_{r \rightarrow 0}\frac{r^2(\cos^2\theta-\sin^2\theta)}{r}=\lim_{r \rightarrow 0}{r(\cos^2\theta-\sin^2\theta)}=\lim_{r \rightarrow 0}{0\cdot(\cos^2\theta-\sin^2\theta)}=0.$$
