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Math Help - Limits and Continuity not Partial Derivatives

  1. #1
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    Limits and Continuity not Partial Derivatives

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

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