Verify the formula [[F.nds = [ div F dV in the Divergence Theorem by evaluating the surface integral and the triple integral. F(x, y, z) = 2xi - yzj + z²k where σ is the paraboloid z = x² + y² capped by the disk x² + y² ≤ 16 in the plane z = 16.

Verify the formula [[F.nds = [ div F dV in the Divergence Theorem by evaluating the surface integral and the triple integral. F(x, y, z) = 2xi - yzj + z²k where σ is the paraboloid z = x² + y² capped by the disk x² + y² ≤ 16 in the plane z = 16.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Question

Verify the formula
11.₁
F.ndS=
- Jª
div F dV
in the Divergence Theorem by evaluating the surface integral and the
triple integral.
F(x, y, z) = 2xi — yzj + z²k
where is the paraboloid z = x² + y² capped by the disk x² + y² ≤ 16
in the plane z = 16.
11.₁
F.ndS =
Jª
div F dV =

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