Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (ln(y) + 16xy3)i + (24x2y2 + x/y)j

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (ln(y) + 16xy3)i + (24x2y2 + x/y)j

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 12E

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Question

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

F(x, y) = (ln(y) + 16xy³)i + (24x²y² + x/y)j

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.)
F(x, y) = (In(y) + 16xy³)i + (24x²y² + x/y)j
f(x, y) =

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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