Question

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = $\nabla f$. (If the vector field is not conservative, enter DNE.) F(x, y) = (2x - 2y) i + (-2x + 14y - 9) j f(x, y) =

Name: determine whether or not f is a conservative vector field if it is find a function f such that f nabla f if the vector field is not conservative enter dne fx y 2x 2y i 2x 14y 9 j fx y 02221
Uploaded: 2023-07-04T22:22:46-08:00
Duration: 4 min 31 s
Channel: Adi S
Description: determine whether or not f is a conservative vector field if it is find a function f such that f nabla f if the vector field is not conservative enter dne fx y 2x 2y i 2x 14y 9 j fx y 02221

          Determine whether or not F is a conservative vector field. If it is, find a function f such that F = $\nabla f$. (If the vector field is not conservative, enter DNE.)
F(x, y) = (2x - 2y) i + (-2x + 14y - 9) j
f(x, y) =

determine whether or not f is a conservative vector field if it is find a function f such that f nabla f if the vector field is not conservative enter dne fx y 2x 2y i 2x 14y 9 j fx y 02221

Added by Brian M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/04/2023

Step 1

A vector field F is conservative if and only if $\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}$. We have $\frac{\partial P}{\partial y} = -2$ and $\frac{\partial Q}{\partial x} = -2$. Since $\frac{\partial P}{\partial y} = \frac{\partial Show more…

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Determine whether or not F is a conservative vector field. If it is, find a function f such that F = $\nabla f$. (If the vector field is not conservative, enter DNE.) F(x, y) = (2x - 2y) i + (-2x + 14y - 9) j f(x, y) =