## Thomas' Calculus 13th Edition

Domain: all real numbers satisfy $x^{2}+y^{2}+z^{2}\ne0$ Range: $(0,\infty)$ Level surfaces: $f(x,y,z)=c$ (positive constant)
Function: $f(x,y,z)=\frac{1}{x^{2}+y^{2}+z^{2}}$ Domain: x, y, and z can be any real numbers except zeros at the same time, that is $x^{2}+y^{2}+z^{2}\ne0$ Range: $f(x,y,z)\gt0$ Level surfaces: $f(x,y,z)=c$ (positive constant) $x^{2}+y^{2}+z^{2}=\frac{1}{c}$ represents a series of spheres. For example, when $c=1$, $x^{2}+y^{2}+z^{2}=1$ is a sphere shown in the figure.