## Thomas' Calculus 13th Edition

Domain: $x: (-\infty,\infty); y: (-\infty,\infty); z: (-\infty,\infty);$ Range: $f(x,y,z): (-\infty,\infty);$ Level surfaces: $f(x,y,z)=c$ (constant)
Function: $f(x,y,z)=x^{2}+4y^{2}+9z^{2}$ Domain: x, y , and z can be any real numbers; Range: $f(x,y,z)\geq0$ Level surfaces: $f(x,y,z)=c$ (constant) $x^{2}+4y^{2}+9z^{2}=c$ represents a series of ellipsoids. For example, when $c=9$, $x^{2}+4y^{2}+9z^{2}=9$ is an ellipsoid as shown in the figure.