Figure

Figure 20

$\lim\limits_{(x, y)\rightarrow (x_{0}, y_{0})}{f(x,y)=L}$ means that for any

$\varepsilon >0,$ there is a

$\delta >0$ , so that whenever

$(x,y) \neq (x_{0},y_{0})$ is within

$\delta$ of

$(x_{0},y_{0})$ , then

$z=f (x,y)$ is within

$\varepsilon$ of

$L$ .