Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Textbook Question

Chapter 14.4, Problem 66E

Channel flow The flow in a long shallow channel is modeled by the velocity field F = (0, 1 – x²), where R = {(x, y): |x| ≤ 1 and |y| = 5}.

a. Sketch R and several streamlines of F.

b. Evaluate the curl of F on the lines x = 0, x = 1 4 , x = 1 2 , and x = 1.

c. Compute the circulation on the boundary of R.

d. How do you explain the fact that the curl of F is nonzero at points of R, but the circulation is zero?

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Chapter 14.4, Problem 65E

Chapter 14.5, Problem 1E

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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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Solution Summary: The author illustrates the region R and several streamlines of the velocity field F=langle 0,1-x2rangle .

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