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Math Help - Does a limit exist?

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by WWTL@WHL View Post
    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.
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  3. #3
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    ...And done. Thank you.
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