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2. Suppose F = (P(x, y, z), Q(x, y, z), R(x, y, z)) and the functions P, Q and R have continuous second order partial derivatives. Prove the identity div (curl F) = 0.

2. Suppose F = (P(x, y, z), Q(x, y, z), R(x, y, z)) and the functions P, Q and R have continuous second order partial derivatives. Prove the identity div (curl F) = 0.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 23E
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2. Suppose F = (P(x, y, z), Q(x, y, z), R(x, y, z)) and the functions P, Q and R have continuous second order partial derivatives. Prove the identity div (curl F) = 0.
Transcribed Image Text:2. Suppose F = (P(x, y, z), Q(x, y, z), R(x, y, z)) and the functions P, Q and R have continuous second order partial derivatives. Prove the identity div (curl F) = 0.
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