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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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(3) Verify the divergence theorem where
(a) F(x, y, z) = 3xi + xyj + 2xzk and E is the cube bounded by the
planes x = 0, x = 1, y = 0, y = 1, z =
(b) F(x, y, z) = x²i+ xyj+ zk and E is the solid bounded by the pa-
raboloid z = 4 – x² – y² and the xy-plane.
0, and z = 1.

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Verify the divergence theorem for F=3i + xy j + x k taken over the region bounded by z = 4 - y^2 , x = 0 , x = 3 , and the xy-plane.
Verify the divergence theorem for F = 3 i+ xy j + x k taken over the region bounded by z = 4 − y2, x = 0, x = 3, and the xy-plane.
Verify the divergence theorem for F = 3 i + xy j + x k taken over the region boundedby z = 4 − y2,x= 0, x = 3, and the xy-plane.
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use the Divergence Theorem to find the outward flux of F across the boundary of the region F = 2xz i - xy j - z2 k D: The wedge cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16
Use the Divergence Theorem to evaluateDouble intergal Z Z of S −→F . d−→SWhere −→F (x, y, z) = 3xy^2 −→i + xe^z −→j + z^3 −→k , and S is the surface of the solid bounded by the cylinder y^2 + z^2 = 1 and the planes x = −1 and x = 3. Show all steps.

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