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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Match the vector fields F with the plots labeled I-IV. Give reasons for your choices.

12. F(x, y) = ⟨y, xy

images

To determine

To match: The vector field F(x,y)=y,xy with the plots labeled as I-IV.

Explanation

Given data:

The vector field F(x,y)=y,xy.

Formula used:

The expression for the length of the two-dimensional vector F=x,y,

|F(x,y)|=x2+y2 (1)

Find the length of F(x,y) using equation (1).

|F(x,y)|=(y)2+(xy)2

Consider a certain interval of x as (2,2) and y as (2,2) to plot F(x,y).

The estimated values of |F(x,y)| and F(x,y) for different values of x and y are shown in Table 1.

Table 1

Quadrant(x,y)|F(x,y)|=(y)2+(xy)2F(x,y)=y,xy
I(0,0)00,0
(1,0)10,1
(2,0)20,2
(0,1)21,1
(1,1)11,0
(0,2)22<

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Chapter 16 Solutions

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