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Chapter 12: Q 55 (page 917)

In Exercises 53-58, determine the level surfaces c=-3,-2,-1,0,1,2,3if they exist for the specified function.

fx,y,z=xy-z.

Short Answer

Expert verified

The level surfaces are planes with the equation x-cy+cz=0;c=-3,-2,-1,0,1,2,3consisting all points on the plane except those points fory=z.

Step by step solution

01

Step 1. Given Information

We have given the following function :-

fx,y,z=xy-z.

We have to determine level surfaces c=-3,-2,-1,0,1,2,3for the given function.

02

Step 2. Determine level surfaces

The given function is :-

fx,y,z=xy-z.

We know that the level surfaces are determined as :-

fx,y,z=c.

That is we have :-

xy-z=c鈬�x=cy-cz鈬�x-cy+cz=0

We know that this is the equation of plane for any value of c. It consists all points on the plane except those for y=z.

So that we can conclude that the level surfaces are the planes with equationx-cy+cz=0forc=-3,-2,-1,0,1,2,3consisting all points except those fory=z.

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