# Does a limit exist?

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• November 6th 2008, 09:59 AM
WWTL@WHL
Does a limit exist?
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. (Crying)
• November 6th 2008, 10:17 AM
Laurent
Quote:

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. (Crying)

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.
• November 6th 2008, 10:31 AM
WWTL@WHL
...And done. Thank you.