Question 5 Let 2 C R be a nonempty open set and let F: 2-R be a vector field of class C. Then, F is conservative in 2 if and only if: (A) N is simply connected and F is irrotational on 2 (B) curl F(x, y, 2) = 0 for every (r, y, 2) E 2 (C) div F(r, y, z) = 0 for every (r, y, z) E2 (D) the work made by F along every close and regular curve y : [a, b] → 2 is null %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Question 5 Let NCR be a nonempty open set and let F: 2→ R' be a vector field of class
C'. Then, F is conservative in 2 if and only if:
(A) N is simply connected and F is irrotational on 2
(B) curl F(x, y, 2) = 0 for every (r, y, z) E 2
(C) div F(r, y, z) = 0 for every (x, y, z) EN
(D) the work made by F along every close and regular curve y: (a, b]→ 2 is null
Transcribed Image Text:Question 5 Let NCR be a nonempty open set and let F: 2→ R' be a vector field of class C'. Then, F is conservative in 2 if and only if: (A) N is simply connected and F is irrotational on 2 (B) curl F(x, y, 2) = 0 for every (r, y, z) E 2 (C) div F(r, y, z) = 0 for every (x, y, z) EN (D) the work made by F along every close and regular curve y: (a, b]→ 2 is null
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