Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

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

Publisher: PEARSON

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Chapter 14.6, Problem 50E

Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward.

50. ∬ S ∇ ln | r | ⋅ n d S , where S is the hemisphere x² + y² + z² = a², for z ≥ 0, and where r = (x, y, z)

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Chapter 14.6, Problem 49E

Chapter 14.6, Problem 51E

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Calculate ff f(x, y, z) d.S for the given surface and function. x² + y² = 25, 0≤ z ≤ 4; f(x, y, z) = e¯² Consider the shown work. To = T, = аф де = д (5 cos 0, 5 sin 0, z) = (-5 sin 0, 5 cos 0, 0) do d -(5 cos 0, 5 sin 0, z) = (0,0,1) дz i N(0, z) = T₁ × T₂ = -5 sin 0 0 ||N(0, z)|| = 5 cos 0 0 2π 4 [[ f(x, y, 2) ds = [²* ["^ e S (5 cos 0)² + (5 sin 0)² + 0 = e² do dz k 0 = (5 cos 0)i + (5 sin 0)j = 1 Identify the first error in the work shown. /25 (cos² 0 + sin²0) The surface integral is written incorrectly. No errors exist in the work shown. The parametrization of the cylinder is incorrect. The normal vector N(0, z) is incorrect. (5 cos 0, 5 sin 0, 0) √25 = 5

2. Write an inline function that returns the value of the function .2 f(t, x) = sin(Va t) cos (Tx) and also works for vectors. Test your function by plotting it over the region [0, 5] × [0, 5]. '

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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Miscellaneous surface integrals Evaluate the following integrals using the method of your choice. Assume normal vectors point either outward or upward . 50. ∬ S ∇ ln | r | ⋅ n d S , where S is the hemisphere x 2 + y 2 + z 2 = a 2 , for z ≥ 0, and where r = ( x , y , z )

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