**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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Answered: Given vector field F = (x + tan-¹(yz),…

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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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.]