I have also an other question...
We have to show that $$\lim_{(x, y) \rightarrow (0, 0)} \frac{\sin xy}{xy}=1$$
Could we show it as followed??
$$\lim_{(x,y) \rightarrow (0,0)} \frac{\sin xy}{xy}$$
$$ x \rightarrow 0, y \rightarrow 0$$
$$\xi=xy \rightarrow 0$$
$$\frac{\sin xy}{xy}=\frac{\sin \xi }{\xi}\overset{ \xi \rightarrow 0 }{\rightarrow } 1$$
Is this correct?? Could I improve something?? @robjohn @ThomasAndrews @DanielFischer