Q5. Consider the vector fieldF(x, y, z) = xi + 2yj + (x² + 4y²)kand the closed surface S made up of two pieces:the paraboloid z = 9- (2²+ y²), with z>0, andits circular base x² + y² = 9, with z = 0.Use the divergence theorem to calculate the total flux of F across the surface S.

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Answered: Q5. Consider the vector field F(x, y,…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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Q5. Consider the vector field F(x, y, z)=xi + 2yj + (x² + 4y²) k and the closed surface S made up of two pieces: the paraboloid z = 9 - (x² + y²), with z > 0, and its circular base x² + y² = 9, with z = 0. Use the divergence theorem to calculate the total flux of F across the surface S.