Chapter 12: Q 50 (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.
$f (x, y) = \cos (x y)$ .

Short Answer

Expert verified

The required level curves $c = - 1, 0, 1$ for the function $f (x, y) = \cos (x y)$ as shown as following :-

For $c = - 3, - 2, 2, 3$ , the function does not exist, so there is no level curves for these points.

Step by step solution

Step 1. Given Information

We have given the following function :-

$f (x, y) = \cos (x y)$

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

Step 2. Graph of level curves

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

We know that the cosine function lies between $- 1 a n d 1$ . So there will be no level curves for $c = - 3, - 2, 2, 3$

That is we have to graph the following equations :-

$\cos (x y) = - 1 \cos (x y) = 0 \cos (x y) = 1$

All of these level curves are hyperbolas.

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of level curves

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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)=cos(xy).

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

Pure Maths

Calculus

Statistics

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

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.
$f (x, y) = \cos (x y)$ .