(a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x − 2y², 2³ – 3y).(b) Use the result in item (a) to determine whether there is a function of three variables x,y, and z such that ox(x, y, z) = x + y + 5z, Oy(x, y, z) = 4x – 2y², and z(x, y, z) = 2³ – 3y.

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(a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x − 2y², 2³ – 3y). -

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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Question

(a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x − 2y², 2³ – 3y).
(b) Use the result in item (a) to determine whether there is a function of three variables x,
y, and z such that ox(x, y, z) = x + y + 5z, Oy(x, y, z) = 4x – 2y², and z(x, y, z) = 2³ – 3y.

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