Chapter 15.1, Problem 39E

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7th Edition

Ron Larson + 1 other

ISBN: 9781337552516

Textbook Problem

In Exercises 37–-44, determine whether the vector field is conservative. If it is, find a potential

function for the vector field.

To determine

Whether the vector field **F**(x,y) **=** x e x 2 y ( 2 y i ^ + x j ^ ) .is conservative. If it is, find a potentialfunction for the vector field.

Explanation

**Given:** The function **F**(x,y) **=**

**Explanation:** A vector field **F**(x,y) **=**

Here, M =

Now, partial differentiating both sides with respect to â€˜yâ€™

=>

and, N=

Now, partial differentiating both sides with respect to â€˜xâ€™

=>

Clearly,

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