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 \(L\).
\(\lim\limits_{(x, y)\rightarrow (x_{0}, y_{0})}{f(x,y)=L}\) 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 \(L\).