Answered: 18. Which of these is a conservative… | bartleby

Algebra and Trigonometry (MindTap Course List)

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 18P

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Question

18. Which of these is a conservative vector field given that all fields are open and simply-connected?
A. F = xy'i+ 2xyj – xzk
B. F = (y + z, x + z,x + y)
C. x In y dx + y In z dy – xyz dz
D. F = (t,t + 2, t²); x = 2t; y =t – 2; z = t2

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1).Evaluate ∮CF•dr, whereF=⟨e^x−y^3,cosy+x^3⟩, and C is a circle of radius 2, centered at the origin, traversed once counterclockwise. 2).Let F(x, y, z) =⟨3x^2y+az, x^3,3x+ 3z^2⟩ be a vector field. For what values of a is F conservative?
Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along thecurve y = x − 2 from (1, −1) to (5, 3). Hint: both should be 276(a) directly(b) using the fundamental theorem for line integrals.
Which of the following statements are true for all vector fields, and which are true only for conservative vector fields? (a) The line integral along a path from P to Q does not depend on which path is chosen. (b) The line integral over an oriented curve C does not depend on how C is parametrized. (c) The line integral around a closed curve is zero. (d) The line integral changes sign if the orientation is reversed. (e ) The line integral is equal to the difference of a potential function at the two endpoints. (f) The line integral is equal to the integral of the tangential component along the curve. (g) The cross partial derivatives of the components are equal. 3
If F is a conservative vector field on a region R, how do you evaluate∫C F ⋅ dr, where C is a path between two points A and B in R?

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