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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 ) = ln ( x y ) c = 0 , ± 1 2 , ± 1 , 3 2 , ± 2

To determine

To graph: The contour map of the surface f(x,y)=ln(xy) using level curves corresponding to c=±0,±12,±1,±32,±2.

Explanation

Given Information:

The provided surface is f(x,y)=ln(xy) and c=±0,±12,±1,±32,±2.

Graph:

Consider the surface,

f(x,y)=ln(xy)

Substitute, 0 for f(x,y) in above equation f(x,y)=ln(xy),

ln(xy)=0xy=1

The level curve is a straight line.

Substitute, 12 for f(x,y) in above equation f(x,y)=ln(xy),

ln(xy)=12xy=e1/2

The level curve is a straight line.

Substitute, 12 for f(x,y) in above equation f(x,y)=ln(xy),

ln(xy)=12xy=e1/2

The level curve is a straight line.

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

ln(xy)=1xy=e

The level curve is a straight line.

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

ln(xy)=1xy=e1

The level curve is a straight line

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