Help evaluating a multivariable limit I tried approaching from y=0, from x=0, from x=y, I also tried using polar coordinates, I always get 0/0. What do I need to do to?
$$\lim_{(x,y)\to(1,1)} \dfrac{(x-y)(x+y-2)}{\sqrt{(x-1)^2+(y-1)^2}}$$
Mulivariable limit problem

Set $x=1+r\cos\theta$, $y=1+\sin\theta$. You obtain
\begin{align}
\frac{(x-y)(x+y-2)}{\sqrt{(x-1)^2+(y-1)^2}}&=\frac{(r\cos\theta-r\sin\theta)(r\cos\theta+r\sin\theta)}{\sqrt{r^2}}\\&=r(\cos^2\theta-\sin^2\theta)=r\cos2\theta,
\end{align}
which tends to $0$ as $r$ tends to $0$.
