Explanation Given: The vector field F = < x 3 , y 3 , z 3 > . Formula used: The flux is calculated using the Divergence theorem, that is, ϕ = ∭ ∇ ⋅ F d V Calculation: The vector field F is written as follows: F = x 3 i ^ + y 3 j ^ + z 3 k ^ Now, calculate the flux using the divergence theorem as follows: ϕ = ∫ F ⋅ n ^ d s = ∭ ∇ ⋅ F d V Here, n ^ is the unit vector and ds is the surface area element. Substitute x 3 i ^ + y 3 j ^ + z 3 k ^ for F and d x d y d z for dV in the equation ϕ = ∭ ∇ ⋅ F d V . ϕ = ∭ ∇ ⋅ ( x 3 i ^ + y 3 j ^ + z 3 k ^ ) d x d y d z = ∭ ( ∂ ∂ x i ^ + ∂ ∂ y j ^ + ∂ ∂ z k ^

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 18.3, Problem 2PQ

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The flux of $F = < x^{3}, y^{3}, z^{3} >$ through every closed surface is positive.

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Chapter 18.3, Problem 1PQ

Chapter 18.3, Problem 3PQ

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The flux of F = < x 3 , y 3 , z 3 > through every closed surface is positive.

Solution Summary: The author calculates the flux of the vector field F using the divergence theorem.

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The flux of $F = < x^{3}, y^{3}, z^{3} >$ through every closed surface is positive.

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Chapter 18 Solutions

The flux of F = &lt; x 3 , y 3 , z 3 &gt; through every closed surface is positive.

Solution Summary: The author calculates the flux of the vector field F using the divergence theorem.

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The flux of F=<x3,y3,z3> through every closed surface is positive.

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Chapter 18 Solutions

The flux of F = < x 3 , y 3 , z 3 > through every closed surface is positive.

The flux of $F = < x^{3}, y^{3}, z^{3} >$ through every closed surface is positive.