# More multi limits

1. Jun 11, 2008

### supercali

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

2. Relevant equations
$$y_{1}=x$$
$$y_2=1/x$$

3. The attempt at a solution
when using $$y_{1}=x$$ we get that the limit is zero
when using this $$y_{2}=1/x$$ 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. Jun 11, 2008

### Vid

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)