Figure 21 
\(\lim\limits_{(x, y, z)\rightarrow (x_{0}, y_{0}, z_0)} f(x,y,z)=L\) means that for any \(\varepsilon >0\), there is a \(\delta >0\), so that whenever \((x,y,z) \neq (x_0,y_0,z_0)\) is within \(\delta\) of \((x_{0},y_{0},z_{0})\), then \(w=f(x,y,z)\) is within \(\varepsilon\) of \(L\).
\(\lim\limits_{(x, y, z)\rightarrow (x_{0}, y_{0}, z_0)} f(x,y,z)=L\) means that for any \(\varepsilon >0\), there is a \(\delta >0\), so that whenever \((x,y,z) \neq (x_0,y_0,z_0)\) is within \(\delta\) of \((x_{0},y_{0},z_{0})\), then \(w=f(x,y,z)\) is within \(\varepsilon\) of \(L\).