Chapter 16.5, Problem 13E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Determine whether or not the vector field is conservative. If it is conservative, find a function *f* such that **F** = ∇*f*.

**13. F**(*x*, *y*, *z*) = *y*^{2}*z*^{3} **i** + 2*xyz*^{3} **j** + 3*xy*^{2}*z*^{2} **k**

To determine

**To find:** Whether the vector field

Explanation

**Given:**

The vector field is

**Formula used:**

The equation of an curl **F** for

**Calculation:**

Substitute

Simplify the equation.

Since **F** is a conservative vector and the domain of **F** is

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