   Chapter 7.3, Problem 39E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Sketching a Contour Map In Exercises 35–42, describe the level curves of the function. Sketch a contour map of the surface using level curves for the given c-values. See Example 3. F u n c t i o n c − V a l u e s f ( x , y ) = x y c = ± 1 ,   ± 2 ,   .   .   . , ± 6

To determine

To graph: The contour map of the surface f(x,y)=xy using level curves corresponding to c=±1,±2,±3,±4,±5±6.

Explanation

Given Information:

The provided surface is z=36x2y2 and c=0,1,2,3.

Graph:

Consider the surface,

f(x,y)=xy

Substitute, ±1 for f(x,y) in above equation f(x,y)=xy,

xy=±1

The level curve is a hyperbola.

Substitute, ±2 for f(x,y) in above equation f(x,y)=xy,

xy=±2

The level curve is a hyperbola.

Substitute, ±3 for f(x,y) in above equation f(x,y)=xy,

xy=±3

The level curve is a hyperbola.

Substitute, ±4 for f(x,y) in above equation f(x,y)=xy,

xy=±4

The level curve is a hyperbola

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