3rd Edition

ISBN: 9780135182543

Author: Briggs

Publisher: PEARSON

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Chapter 17.6, Problem 47E

Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface.

47. F = r / | r | 3 across the sphere of radius a centered at the origin, where r = 〈x, y, z〉; normal vectors point outward.

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Chapter 17.6, Problem 46E

Chapter 17.6, Problem 48E

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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Chapter 17 Solutions

CALCULUS:EARLY TRANSCENDENTALS-PACKAGE

Ch. 17.1 - If the vector field in Example 1c describes the...Ch. 17.1 - In Example 2, verify that g(x, y). G(x, y) = 0. In...Ch. 17.1 - Find the gradient field associated with the...Ch. 17.1 - How is a vector field F = f, g, h used to describe...Ch. 17.1 - Sketch the vector field F = x, y.Ch. 17.1 - Prob. 3E Ch. 17.1 - Given a differentiable, scalar-valued function ,...Ch. 17.1 - Interpret the gradient field of the temperature...Ch. 17.1 - Show that all the vectors in vector field...Ch. 17.1 - Sketch a few representative vectors of vector...

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