Answered: Let F(x, y, z) =< x, y, z>, E is the…

Let F(x, y, z) =< x, y, z>, E is the unit ball x² + y² + z² ≤ 1. Verify the Divergence Theorem by evaluating the following directly. (a). ff divF dv. (b). ffs F. ds.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...

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Let F(x, y, z) =< x, y, z>, E is the unit ball x² + y² + z² ≤ 1. Verify the Divergence Theorem by evaluating the
following directly.
(a). fff divF dv.
(b). ffs F.ds.

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Step 1: Finding div of the given vector field.

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Step 2: The triple integral.

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Step 3: Flux across the surface S.

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Step 4: Divergence theorem

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