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Chapter 12: Problem 8

How many axes (or how many dimensions) are needed to graph the level surfaces of \(w=f(x, y, z) ?\) Explain.

Short Answer

Expert verified
Answer: To graph the level surfaces of the given function \(w = f(x, y, z)\), three axes (dimensions) are needed, which correspond to the x, y, and z coordinates of points in the level surfaces.

Step by step solution

01

Understand level surfaces

A level surface of a function is a three-dimensional shape in space on which all points have the same function value. In the given function \(w=f(x, y, z)\), the level surfaces are formed by the set of all points \((x, y, z)\) that satisfy the equation \(w = f(x, y, z)\) for a constant value of \(w\). To represent these surfaces, we need a coordinate system that can represent three dimensions: x, y, and z.
02

Determine the number of axes needed

Since the level surfaces are three-dimensional shapes, we need three axes (i.e., three dimensions) to represent them graphically. The axes correspond to the x, y, and z coordinates of points in the level surfaces.
03

Conclusion

To graph the level surfaces of the given function \(w = f(x, y, z)\), three axes (dimensions) are needed, which correspond to the x, y, and z coordinates of points in the level surfaces.

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Most popular questions from this chapter

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