Limits and Continuity not Partial Derivatives

**genlovesmusic09** · March 28th 2010, 08:58 AM

$f(x,y) = \left\{ \begin{gathered} \frac{{{x^2} - {y^2}}} {{\sqrt {{x^2} + {y^2}} }}for(x,y) \ne (0,0) \hfill \\ 1for(x,y) = 0 \hfill \\ \end{gathered} \right. $

I tried multiplying the first part by sq rt x^2 + y^2 but I don't know where to continue from there

**running-gag** · March 28th 2010, 11:19 AM

Hi

$\frac{|x^2 - y^2|}{\sqrt {x^2 + y^2}} \leq \frac{x^2 + y^2}{\sqrt {x^2 + y^2}}$

$\frac{|x^2 - y^2|}{\sqrt {x^2 + y^2}} \leq \sqrt {x^2 + y^2}$

Therefore the limit in (0,0) is 0

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