## Thomas' Calculus 13th Edition

Domain: all real numbers Range: $0\lt f(x,y,z)\leq1$ Level surfaces: $f(x,y,z)=c$ (constant in $(0,1]$)
Function: $f(x,y,z)=\frac{1}{x^{2}+y^{2}+z^{2}+1}$ Domain: x, y, and z can be any real numbers Range: $0\lt f(x,y,z)\leq1$ Level surfaces: $f(x,y,z)=c$ (constant in $(0,1]$) $x^{2}+y^{2}+z^{2}=\frac{1}{c}-1$ represents a series of spheres. For example, when $c=\frac{1}{2}$, $x^{2}+y^{2}+z^{2}=1$ is a sphere shown in the figure.