Q2.(a)Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k.(i)Determine whether if F is conservative or not.(ii)Find the potential function of F and evaluate it at the point A(1,3, 2).(b)Given a vector field F = 5(x2 + y?)i+ 2xyj – 3zk, evaluate fff, V. FdV forwhich the solid D is formed by a paraboloid x² + y2 + z = 10 in the firstoctant.

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Answered: Q2. (a) Given a vector field, F = 2xyi…

Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is conservative or not. (ii) Find the potential function of F and evaluate it at the point A(1,3, 2).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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Question

Q2.
(a)
Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k.
(i)
Determine whether if F is conservative or not.
(ii)
Find the potential function of F and evaluate it at the point A(1,3, 2).
(b)
Given a vector field F = 5(x2 + y?)i+ 2xyj – 3zk, evaluate fff, V. FdV for
which the solid D is formed by a paraboloid x² + y2 + z = 10 in the first
octant.

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