Q 48 In Exercises 43-52, sketch the l... [FREE SOLUTION]

Chapter 12: Q 48 (page 917)

In Exercises $43 - 52$ , sketch the level curves $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y) = x^{2} - y^{2}$ .

Short Answer

Expert verified

The required level curves $c = - 3, - 2, - 1, 0, 1, 2, 3$ for the function $f (x, y) = x^{2} - y^{2}$ as shown as following :-

Step by step solution

Step 1. Given Information

We have given the following function :-

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

We have to graph the level curveslocalid="1653210113982" $c = - 3, - 2, - 1, 0, 1, 2, 3$ for this function.

Step 2. Graph of level curves

For each value of $c$ , the level curve is the graph of the equation $f (x, y) = c$ .

That is we have to graph the following equations :-

$x^{2} - y^{2} = - 3, x^{2} - y^{2} = - 2, x^{2} - y^{2} = - 1, x^{2} - y^{2} = - 0, x^{2} - y^{2} = 1, x^{2} - y^{2} = 2 a n d x^{2} - y^{2} = 3,$

As these level curves are hyperbolas.

Then we have the following graph of these level curves :-

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91影视

In Exercises $43 - 52$ , sketch the level curves $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y) = x^{2} - y^{2}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of level curves

One App. One Place for Learning.

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91影视

In Exercises 43-52, sketch the level curves c=-3,-2,-1,0,1,2,3if they exist for the specified function.f(x,y)=x2-y2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of level curves

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Probability and Statistics

Decision Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Exercises $43 - 52$ , sketch the level curves $c = - 3, - 2, - 1, 0, 1, 2, 3$ if they exist for the specified function.
$f (x, y) = x^{2} - y^{2}$ .