Evaluate the outward Aux of the vector fieldF=… (2.x- 5e" + sin(2²), –4ry +In(x*), 5z – 32'y)F =across the boundary of the regionW = {(r, y, z) E R : a² + y? + z? < 9, Jr| 2 1. |y| 2 1, |2| 2 1}.

Given F=2x2-5ey+sinz2,-4xy+lnx4,5z-3x2y6

Answered: F = (2x- 5e" + sin(z'), –4ry + In(r'),…

F = (2x- 5e" + sin(z'), –4ry + In(r'), 5z - 3r°y) %3D across the boundary of the region W = {(r, y, z) E R : r + y? + 2? < 9, Jr| 2 1. y| 2 1, |2| 2 1}.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 28E

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Question

Evaluate the outward Aux of the vector field F=…

(2.x- 5e" + sin(2²), –4ry +
In(x*), 5z – 32'y)
F =
across the boundary of the region
W = {(r, y, z) E R : a² + y? + z? < 9, Jr| 2 1. |y| 2 1, |2| 2 1}.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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