3. (Section 17.6, 17.8) Consider S₁x² + y² = 9, S₂: z=0, (a) Graph surface S. = xî + yĵ+ (2² − 1)k. Let S be the surface of the solid bounded by S3 : z = 2.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 21E
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3. (Section 17.6, 17.8) Consider F = xî + yĵ + (z² − 1)k. Let S be the surface of the solid bounded by
S₁: x² + y² = 9, S₂: z=0, S3 : z = 2.
(a) Graph surface S.
Transcribed Image Text:3. (Section 17.6, 17.8) Consider F = xî + yĵ + (z² − 1)k. Let S be the surface of the solid bounded by S₁: x² + y² = 9, S₂: z=0, S3 : z = 2. (a) Graph surface S.
(b) Evaluate F.ds to determine the downward flux through S₂.
S₂
(c) Evaluate [.ds to determine the upward flux through S3.
S3
(d) Use the Divergence Theorem to calculate the outward flux through the closed surface.
Transcribed Image Text:(b) Evaluate F.ds to determine the downward flux through S₂. S₂ (c) Evaluate [.ds to determine the upward flux through S3. S3 (d) Use the Divergence Theorem to calculate the outward flux through the closed surface.
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