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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.

14. F(x, y) = ⟨cos(x + y), x

images

To determine

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

Explanation

Given data:

F(x,y)=cos(x+y),x

Formula used:

Consider a two-dimensional vector F=x,y .

Write the expression for length of the two dimensional vector.

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

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

|F(x,y)|=(cos(x+y))2+(x)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)|=(cos(x+y))2+(x)2 F(x,y)=cos(x+y),x
I (0,0) [cos(0)]2 cos(0),0
(1,0) [cos(1)]2+1 cos(1),1
(2,0) [cos(2)]2+4 cos(2),2
(0,1) [cos(1)]2 cos(1),0
(1,1) [cos(2)]2+1 cos(2),1
(0,2) [cos(2)]2 cos(2),0
(2,2) [cos(4)]2+4 cos(4),2

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Chapter 16 Solutions

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