Multivariable Calculus - Very Basic Approach   The Level Sets of  f (x,y,z) = 2x2 + y2 + 3z2

Here is an example which illustrates how the collection of all points in a level set form an object in 3-space.

Each level set is a complete ellipsoid. In this contour map, level sets have been cut open to give a view of several of them.
 

Return to the main document on level sets.