Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

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

Publisher: PEARSON

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Textbook Question

Chapter 14.1, Problem 40E

Equipotential curves Consider the following potential functions and graphs of their equipotential curves.

a. Find the associated gradient field F = ▿ϕ.

b. Show that the vector field is orthogonal to the equipotential curve at the point (1, 1). Illustrate this result on the figure.

c. Show that the vector field is orthogonal to the equipotential curve at all points (x, y).

d. Sketch two flow curves representing F that are everywhere orthogonal to the equipotential curves.

40. ϕ (x, y) = x²+ 2y²

Chapter 14.1, Problem 40E, Equipotential curves Consider the following potential functions and graphs of their equipotential

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Chapter 14.1, Problem 39E

Chapter 14.1, Problem 41E

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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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