Thread: Limits and Continuity not Partial Derivatives

1. Limits and Continuity not Partial Derivatives

$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

2. 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