Given vector field F = (x + tan-¹(yz), 2y - 8e12xz, 4z3 - 10 ln(2x+y)). S is the surface defined as the part of the cone z = √√x² + y² that is under the plane z = 4. Use the divergence theorem to find the outward flux over S. [Extra going on here.]
Given vector field F = (x + tan-¹(yz), 2y - 8e12xz, 4z3 - 10 ln(2x+y)). S is the surface defined as the part of the cone z = √√x² + y² that is under the plane z = 4. Use the divergence theorem to find the outward flux over S. [Extra going on here.]
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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![**Problem #4:**
Given the vector field \( \mathbf{F} = \langle x + \tan^{-1}(yz), 2y - 8e^{12xz}, 4z^3 - 10 \ln(2x + y) \rangle \). The surface \( S \) is defined as the part of the cone \( z = \sqrt{x^2 + y^2} \) that is under the plane \( z = 4 \).
Use the divergence theorem to find the outward flux over \( S \).
[Extra going on here.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba09805e-c69e-42c2-a695-6eaaf9d4ee4f%2Fb3baf80d-038c-410e-86c2-97f4afc0950f%2Ft4ob23n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem #4:**
Given the vector field \( \mathbf{F} = \langle x + \tan^{-1}(yz), 2y - 8e^{12xz}, 4z^3 - 10 \ln(2x + y) \rangle \). The surface \( S \) is defined as the part of the cone \( z = \sqrt{x^2 + y^2} \) that is under the plane \( z = 4 \).
Use the divergence theorem to find the outward flux over \( S \).
[Extra going on here.]
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