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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?

Martin Sleziak
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    Duplicate: [$\lim\limits_{(x,y) \to (0,0)} \dfrac{xy}{|x|+|y|}$](https://math.stackexchange.com/q/307845/201168). (*Found using [Approach0.xyz](https://approach0.xyz/)*) – Workaholic Dec 03 '16 at 19:03

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