Consider $$\lim_{(x,y)\to(0,0)} \frac{xy}{|x|+|y|}$$
I tried the following technique but couldn't work it out
define $p=(x,y)$ we end up with the following inequalities :
$$|p|^2=x^2+y^2\\ |x|≤|p| \\ |y|≤ |p|$$
But couldn't use them at all couldn't find a boundary. What should I do? What would you recommend?
