$\lim_{(x,y) \rightarrow (0,0)} \frac{xy}{|x|+|y|}$

Question

I have a question. I want to check whether the following limit exists:

$$\lim_{(x,y) \rightarrow (0,0)} \frac{xy}{|x|+|y|}.$$

I have already searched on the internet and they say many different things. In my own book there stood that it doesn't exist. Is that true? And how do you show that it doesn't or does exist by this limit?

Thank you

Possible Dup[licate http://math.stackexchange.com/questions/307845/wrong-wolframalpha-limit-fx-y-frac-xyxy-for-x-y-to0-0 — Juniven Acapulco, Jan 27 '17 at 11:16

score 2 · Answer 1 · answered Jan 27 '17 at 11:25

2

Fill in details:

$$\left|\frac{xy}{|x|+|y|}\right|\le\frac{|xy|}{|x|}=|y|\xrightarrow[(x,y)\to(0,0)]{}0$$

answered Jan 27 '17 at 11:25

DonAntonio

214,715

$\lim_{(x,y) \rightarrow (0,0)} \frac{xy}{|x|+|y|}$

1 Answers1