Determine whether the following statements are true and give an explanation or counterexample. a. The work required

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Determine whether the following statements are true and give an explanation or counterexample.

a. The work required to move an object around a closed curve C in the presence of a vector force field is the circulation of the vector field on the curve.

b. If a vector field has zero divergence throughout a region (on which the conditions of Green’s Theorem are met), then the circulation on the boundary of that region is zero.

c. If the two-dimensional curl of a vector field is positive throughout a region (on which the conditions of Green’s Theorem are met), then the circulation on the boundary of that region is positive (assuming counterclockwise orientation).

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Calculus For Scientists And Engineers Early Transcendentals

ISBN: 9780321849212

1st Edition

Authors: William L Briggs, Bernard Gillett, Bill L Briggs, Lyle Cochran

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