Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 14.3, Problem 54E

Radial Fields in ¡³ are conservative Prove that the radial field F = r | r | p , where r = 〈x, y, z〉 and p is a real number, is conservative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin?

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Chapter 14.3, Problem 53E

Chapter 14.3, Problem 55E

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Radial fields in R are conservative Prove that the radial field where r = (x, y, z) and p is a real number, is conser- vative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin? F

The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is independent of z and its z-component is 0.) (a) Is div(F) positive, negative, or zero at P? Explain. div(F) is --Select--- because the vectors that start near P are -Select--- (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at P? O curl(F) + 0. At P the curl(F) points in the direction of positive x. O curl(F) + 0. At P the curl(F) points in the direction of negative x. O curl(F) + 0. At P the curl(F) points in the direction of positive y. O curl(F) + 0. At P the curl(F) points in the direction of negative y. O curl(F) + 0. At P the curl(F) points in the direction of positive z. O curl(F) + 0. At P the curl(F) points in the direction of negative z. O curl(F) = 0 those that end near P.

6 The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is independent of z and its z-component is 0.) (a) Is div(F) positive, negative, or zero at P? Explain. div(F) is |---Select---because the vectors that start near Pare ---Select--- (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at P? O curl(F) + 0. At P the curl(F) points in the direction of positive x. O curl(F) + 0. At P the curl(F) points in the direction of negative x. O curl(F) + 0. At P the curl(F) points in the direction of positive y. O curl(F) = 0. At P the curl(F) points in the direction of negative y. O curl(F) + 0. At P the curl(F) points in the direction of positive z. O curl(F) = 0. At P the curl(F) points in the direction of negative z. O curl(F) = 0 those that end near P.

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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Radial Fields in ¡ 3 are conservative Prove that the radial field F = r | r | p , where r = 〈 x, y, z 〉 and p is a real number, is conservative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin?

Solution Summary: The author explains that a radial field F= rleft|tp and p is real number is conservative on any region not containing the origin

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