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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If F and G are vector fields and div F = div G, then F = G.

To determine

Whether the statement “If F and G are vector fields and divF=divG , then F=G ” is true or false.

Explanation

Formula used:

Write the expression for divergence.

divF=Px+Qy+Rz (1)

Consider the two different three-dimensional vector fields as follows.

F=x,0,0G=0,0,z

Substitute x for P, 0 for Q and 0 for R in equation (1),

divF=(x)x+(0)y+(0)z=1+0+0=1

Modify equation (1) as follows

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Chapter 16 Solutions

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