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Chapter 12: Q 53 (page 917)

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

localid="1653228727636" fx,y,z=x+2y+3z.

Short Answer

Expert verified

The level surfaces are the planes with equations

x+2y+3z=c;c=-3,-2,-1,0,1,2,3.

Step by step solution

01

Step 1. Given information

We have given the following function :-

fx,y,z=x+2y+3z.

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=x+2y+3z

We know that the level surfaces are determined as :-

fx,y,z=c.

That is we have :-

x+2y+3z=c

We know that this is the equation of plane for any value of c.

So that we can conclude that the level surfacesare the planes with equation x+2y+3z=cfor c=-3,-2,-1,0,1,2,3.

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