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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Finding a Conservative Vector Field In Exercises 3-6, find the conservative vector field for the potential function by finding its gradient.

f ( x , y , z ) = x 2 e y z

To determine

To calculate: The conservative vector field for the potential function f(x,y,z)=x2eyz.

Explanation

Given:

The potential function is: f(x,y,z)=x2eyz

Formula used:

The conservative vector field for the potential function f(x,y,z) is given by,

f(x,y)=fxi^+fyj^+fzk^

Chain rule,

xf(g(x))=f(x)xg(x)

Calculation:

In order to compute the vector field for the provided potential function f(x,y), first find the gradient of the function f.

Since F(x,y,z)=f.

Now,

f(x,y)=fxi^+fyj^+fzk^

Substitute the value of the function f(x,y,z)=x2eyz in above formula, to get,

f(x,y,z)=x(x2eyz)i^+y(x2eyz)j

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Chapter 15 Solutions

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P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ECh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-46RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-50RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-61RECh-15 P-62RECh-15 P-63RECh-15 P-64RECh-15 P-65RECh-15 P-66RECh-15 P-67RECh-15 P-68RECh-15 P-69RECh-15 P-70RECh-15 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