Let F(x, y,z) = and let σ be the portion of z = 1 − x^2 − y^2 that is on or above the xy-plane oriented by upward normals. 1. Sketch σ accurately. 2. Parametrize sigma. 3. Sketch the associated Ruv for the chosen parameters (u, v). 4. Find the flux Φ of F through σ.
Let F(x, y,z) = and let σ be the portion of z = 1 − x^2 − y^2 that is on or above the xy-plane oriented by upward normals. 1. Sketch σ accurately. 2. Parametrize sigma. 3. Sketch the associated Ruv for the chosen parameters (u, v). 4. Find the flux Φ of F through σ.
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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Question
Let F(x, y,z) = <x, y, 2z> and let σ be the portion of
z = 1 − x^2 − y^2
that is on or above the xy-plane oriented by upward normals.
1. Sketch σ accurately.
2. Parametrize sigma.
3. Sketch the associated Ruv for the chosen parameters (u, v).
4. Find the flux Φ of F through σ.
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