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More multi limits

  1. Jun 11, 2008 #1
    1. The problem statement, all variables and given/known data
    solve
    [tex] {\lim }\limits_{\scriptstyle x \to 0 \hfill \atop
    \scriptstyle y \to 0 \hfill} (xy\ln \left( {x^2 + y^2 } \right)) [/tex]

    2. Relevant equations
    [tex]y_{1}=x[/tex]
    [tex]y_2=1/x[/tex]

    3. The attempt at a solution
    when using [tex]y_{1}=x[/tex] we get that the limit is zero
    when using this [tex]y_{2}=1/x[/tex] we get that the limit is infinity
    thus the limit does not ! exist.
    i dont know if it is ok to use these 2 paths i some how have a feeling that the second one is wrong
    thanks for the help
     
  2. jcsd
  3. Jun 11, 2008 #2

    Vid

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    Convert it to polar and let r->0. You get that the limit is zero. Also, the whole idea of using a path is to show the limits do not exist by showing that if you approach the point 0,0 along different paths then you get different limits. y = 1/x never approaches (0,0)
     
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