Does a limit exist?

**WWTL@WHL** · November 6th 2008, 09:59 AM

Question:

Does $lim_{x \to 0} \left(g(x)\right)$ exist, when

$g ( x_1 , x_2 )^T = \frac{x_1 x_2}{ |{x_1}| + |{x_2}|}$

I have no clue. Please help.

**Laurent** · November 6th 2008, 10:17 AM

Originally Posted by WWTL@WHL

Question:

Does $lim_{x \to 0} \left(g(x)\right)$ exist, when

$g ( x_1 , x_2 )^T = \frac{x_1 x_2}{ |{x_1}| + |{x_2}|}$

I have no clue. Please help.

You should try to find a simple upper bound for $|g(x_1,x_2)|$ which converges to 0 when $(x_1,x_2)\to 0$ . For instance, a possibility is to use the fact that $|x_1|+|x_2|\geq |x_2|$ . I let you try that.

**WWTL@WHL** · November 6th 2008, 10:31 AM

...And done. Thank you.

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