Chapter 16, Problem 5RQ

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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** = *P* **i** + *Q* **j** and *P _{y} = Q_{x}* in an open region

To determine

Whether the statement “If
*D*, then **F** is conservative” is true or false.

Explanation

If every simple closed curve in *D* encloses only points that are present in *D* then, the connected region is known as simply-connected region.

Consider the vector field
*D.*

If *P* and *Q* are continuous first-order partial derivatives and
*D* then the vector function **F** is conservative

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