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Chapter 12: Q. 2 (page 987)

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.

* a level surface for f (x, y, z).

Short Answer

Expert verified

For a function of three variables, a level set is a surface of three-dimensional space that we will call a level surface.

Step by step solution

01

Step 1. Given Information.

A level surface for f (x, y, z).

02

Step 2. Definition.

For a function of three variables, a level set is a surface in three-dimensional space that we will call a level surface. For a constant value c in the range of f(x, y, z), the level surface of f is the implicit surface given by the graph of c=f(x,y,z).

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