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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

how do i solve the attached calculus problem?

For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) F = 2yzi + (2xz+2²)j + (2xy + 2yz) k:
curl F =
Fis a gradient field
(b) G = (2xy + yz)i + (2x² + z²) j+5xz k:
curl G =
Gis not a gradient field
(c) Ĥ = (4xy + 2x³) i + (2x² + 2²) j + (2yz — 52) k:
curl Ĥ =
His a gradient field

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