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If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y, z)) > 0) fo - all (x, y, z).

If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y, z)) > 0) fo - all (x, y, z).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Let be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If h has continuous partial derivatives on R, and P (x, y, z) is continuous on C, then ſf P(x, y, z)dS = ſf P(h(y, z), y, z),√ √/h? (y, z) + h² (y, z) + 1 dA, C R where dA dydz or dA dzdy. = =
Transcribed Image Text:Let be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If h has continuous partial derivatives on R, and P (x, y, z) is continuous on C, then ſf P(x, y, z)dS = ſf P(h(y, z), y, z),√ √/h? (y, z) + h² (y, z) + 1 dA, C R where dA dydz or dA dzdy. = =
If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y — z, z — x, x − y), then div(curlG (x, y, z)) > 0) for all (x, y, z).
Transcribed Image Text:If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y — z, z — x, x − y), then div(curlG (x, y, z)) > 0) for all (x, y, z).
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