Q 57 In Exercises 53-58, determine th... [FREE SOLUTION]

Chapter 12: Q 57 (page 917)

In Exercises $53 - 58$ , determine the level surfaces $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y, z) = x^{2} + y^{2} + z^{2}$ .

Short Answer

Expert verified

The level surfaces are determined by the equation $x^{2} + y^{2} + z^{2} = c$ . For $c = 0$ , $x^{2} + y^{2} + z^{2} = 0$ represents the origin of 3-D plane.

Also the level surfaces are sphere with equation :-

$x^{2} + y^{2} + z^{2} = c; c = 1, 2, 3$ .

For $c = - 3, - 2, - 1$ level surfaces are undefined.

Step by step solution

Step 1. Given Information

We have given the following function :-

$f (x, y, z) = x^{2} + y^{2} + z^{2}$ .

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

Step 2. Determine level surfaces

The given function is :-

$f (x, y, z) = x^{2} + y^{2} + z^{2}$ .

We know that the level surfaces are determined as :-

$f (x, y, z) = c$ .

That is we have :-

$x^{2} + y^{2} + z^{2} = c$ .

This is the equation of sphere.

So the level surfaces are undefined for $c = - 3, - 2, - 1$ as radius of sphere cannot be negative.

Also for $c = 0$ , $x^{2} + y^{2} + z^{2} = 0$ represents the origin of 3-D plane.

So that we have :-

The level surfaces are sphere with the equation $x^{2} + y^{2} + z^{2} = c$ for role="math" $c = 1, 2, 3$ .

For $c = 0$ , level surface is origin.

For $c = - 3, - 2, - 1$ the level surfaces are undefined.

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91影视

In Exercises $53 - 58$ , determine the level surfaces $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y, z) = x^{2} + y^{2} + z^{2}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine level surfaces

One App. One Place for Learning.

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91影视

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=x2+y2+z2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine level surfaces

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Exercises $53 - 58$ , determine the level surfaces $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y, z) = x^{2} + y^{2} + z^{2}$ .