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Verify the Divergence Theorem for the vector field F(x, y, z) = zi+yj+rk where E is the solid ball x² + y² + z² ≤ 16, by computing the following: (a) Compute [[ FdS, where S is surface of the sphere x² + y² + z2 = 16, oriented outward. •SSS₁² (b) Compute div (F) dV, where E is the solid ball x² + y² + z² ≤ 16.

Verify the Divergence Theorem for the vector field F(x, y, z) = zi+yj+rk where E is the solid ball x² + y² + z² ≤ 16, by computing the following: (a) Compute [[ FdS, where S is surface of the sphere x² + y² + z2 = 16, oriented outward. •SSS₁² (b) Compute div (F) dV, where E is the solid ball x² + y² + z² ≤ 16.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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13. Verify the Divergence Theorem for the vector field F(x, y, z) = zi+yj + xk where E is the solid ball x² + y² + z² ≤ 16, by computing the following: (a) Compute (b) Compute 11.x F. ds, where S is surface of the sphere x² + y² + z2 = 16, oriented outward. div (F) dV, where E is the solid ball x² + y² + z² ≤ 16. E
Transcribed Image Text:13. Verify the Divergence Theorem for the vector field F(x, y, z) = zi+yj + xk where E is the solid ball x² + y² + z² ≤ 16, by computing the following: (a) Compute (b) Compute 11.x F. ds, where S is surface of the sphere x² + y² + z2 = 16, oriented outward. div (F) dV, where E is the solid ball x² + y² + z² ≤ 16. E
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