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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 ) = x x 2 + y 2 c = ± 1 2 , ± 1 , 3 2 , ± 2

To determine

To graph: The contour map of the surface f(x,y)=xx2+y2 using level curves corresponding to c=±12,±1,±32,±2.

Explanation

Given Information:

The provided surface is f(x,y)=xx2+y2 and c=±12,±1,±32,±2.

Graph:

Consider the surface,

f(x,y)=xx2+y2

Substitute, 12 for f(x,y) in above equation f(x,y)=xx2+y2,

xx2+y2=122x=x2+y2(x1)2+y2=1

The level curve is a circle.

Substitute, 12 for f(x,y) in above equation f(x,y)=xx2+y2,

xx2+y2=122x=x2+y2(x+1)2+y2=1

The level curve is a circle.

Substitute, 1 for f(x,y) in above equation f(x,y)=xx2+y2,

xx2+y2=1x=x2+y2(x12)2+y2=14

The level curve is a circle.

Substitute, 1 for f(x,y) in above equation f(x,y)=xx2+y2,

xx2+y2=1x=x2+y2(x+12)2+y2=14

The level curve is a circle.

Substitute, 32 for f(x,y) in above equation f(x,y)=xx2+y2,

xx2+y2=322x=3(x2+y2)(x+32)2+y2=19

The level curve is a circle

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