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3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

Advanced Engineering Mathematics
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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3. Consider the radial vector field F = (r, y, z). Is the upward (outward) flux of the field greater across the hemisphere z +y + z² = 1, for z 2 0, or across the paraboloid 1-r2-y2, for z 0? Note that the two surfaces have the same base in the ry- plane and the same high point (0,0, 1). Use the explicit description of the hemisphere and a parametric description for the paraboloid.
Transcribed Image Text:3. Consider the radial vector field F = (r, y, z). Is the upward (outward) flux of the field greater across the hemisphere z +y + z² = 1, for z 2 0, or across the paraboloid 1-r2-y2, for z 0? Note that the two surfaces have the same base in the ry- plane and the same high point (0,0, 1). Use the explicit description of the hemisphere and a parametric description for the paraboloid.
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