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Use the divergence theorem to evaluate the flux of F across S where F(x, y, z) = (3x² + z)i+ (x + 3y")j+ (3z³ + y)k and S is the boundary of the solid region bounded by the cone z? = x² + y² , z 2 0 and the hemisphere z = 5- x² – y² with outward unit normal.

Use the divergence theorem to evaluate the flux of F across S where F(x, y, z) = (3x² + z)i+ (x + 3y")j+ (3z³ + y)k and S is the boundary of the solid region bounded by the cone z? = x² + y² , z 2 0 and the hemisphere z = 5- x² – y² with outward unit normal.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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QUESTION 4 Use the divergence theorem to evaluate the flux of F across S where F(x, y,z) = (3x³ + z)i+ (x + 3y)j+ (3z3 +y)k and S is the boundary of the solid region bounded by the cone z? = x? + y? , z 2 0 and the hemisphere z = 5-x² – y² with outward unit normal.
Transcribed Image Text:QUESTION 4 Use the divergence theorem to evaluate the flux of F across S where F(x, y,z) = (3x³ + z)i+ (x + 3y)j+ (3z3 +y)k and S is the boundary of the solid region bounded by the cone z? = x? + y? , z 2 0 and the hemisphere z = 5-x² – y² with outward unit normal.
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