Q 56 In Exercises 53-58, determine th... [FREE SOLUTION]

Chapter 12: Q 56 (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.
$f (x, y, z) = \frac{x^{2} + y^{2}}{z}$ .

Short Answer

Expert verified

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

Also the level surfaces are circular paraboloid with equation $x^{2} + y^{2} = c z; c = - 3, - 2, - 1, 1, 2, 3$ .

Step by step solution

Step 1. Given Information

We have given the following function :-

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

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 :-

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

We know that the level surfaces are determined as :-

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

That is we have :-

$\frac{x^{2} + y^{2}}{z} = c 鈬� x^{2} + y^{2} = c z$

For $c = 0$ , it becomes :-

$x^{2} + y^{2} = 0$ . It represents the z-axis in 3-D plane.

For all other values of $c = - 3, - 2, - 1, 1, 2, 3$ , the level surfaces $x^{2} + y^{2} = c z$ are circular paraboloid.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine level surfaces

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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+y2z.

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

Pure Maths

Calculus

Logic and Functions

Applied Mathematics

Mechanics Maths

Geometry

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