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More multi limits

  • Thread starter supercali
  • Start date
  • #1
53
0

Homework Statement


solve
[tex] {\lim }\limits_{\scriptstyle x \to 0 \hfill \atop
\scriptstyle y \to 0 \hfill} (xy\ln \left( {x^2 + y^2 } \right)) [/tex]

Homework Equations


[tex]y_{1}=x[/tex]
[tex]y_2=1/x[/tex]

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
 

Answers and Replies

  • #2
Vid
401
0
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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