a. Explanation Formula used: The two dimensional curl of the vector field is δ g δ x − δ f δ y . Calculation: The curl for the vector field F = 〈 y , x 〉 with f ( x , y ) = y and g ( x , y ) = x . δ g δ x − δ f b. To determine To evaluate: The two integrals involved in Green’s theorem and check the consistency. c. To determine To check: Is the vector field conservative?

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 14.4, Problem 12E

To determine

To compute: The two dimensional curl of the vector field F=〈y,x〉 .

To determine

To evaluate: The two integrals involved in Green’s theorem and check the consistency.

To determine

To check: Is the vector field conservative?

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Chapter 14.4, Problem 11E

Chapter 14.4, Problem 13E

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Chapter 14 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 14.1 - How is a vector field F = f, g, h used to describe...Ch. 14.1 - Sketch the vector field F = x, y.Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Interpret the gradient field of the temperature...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...Ch. 14.1 - Two-dimensional vector fields Sketch the following...

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The two dimensional curl of the vector field F = 〈 y , x 〉 .

Solution Summary: The author explains how the two dimensional curl of the vector field F=langle y,xrangle is 0. The two integrals involved in Green's theorem result in zero and consistency holds

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To compute: The two dimensional curl of the vector field F=〈y,x〉 .

To evaluate: The two integrals involved in Green’s theorem and check the consistency.

To check: Is the vector field conservative?

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Chapter 14 Solutions