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EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION Using this equation, we have j a curl F = Vx F = i k ax ду az 5xyz -y? 4xz ду az (Sxyz) – (4x2) K + ду (-2y - (0 - 4x)j + (5yz - 0)k This shows that curl F = v0 and so F is not conservative.

EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION Using this equation, we have j a curl F = Vx F = i k ax ду az 5xyz -y? 4xz ду az (Sxyz) – (4x2) K + ду (-2y - (0 - 4x)j + (5yz - 0)k This shows that curl F = v0 and so F is not conservative.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION Using this equation, we have i a curl F = Vx F = ax dz 4xz 5xyz -y? 4xz) az ду az ax + ax ду -2y - (0 - 4x)j + (5yz – 0)k This shows that curl v 0 and so F is not conservative.
Transcribed Image Text:EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION Using this equation, we have i a curl F = Vx F = ax dz 4xz 5xyz -y? 4xz) az ду az ax + ax ду -2y - (0 - 4x)j + (5yz – 0)k This shows that curl v 0 and so F is not conservative.
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