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Which of the following statements is incorrect, assuming that all second-order partial derivatives exist and are continuous? Assume that "o* can stand for eithier a scalar or a vector, depending on context. O an fis a scalar function, then the curl of the gradient of f must be 0. O br s is a scalar function, then the divergence of the gradient of / must be 0. O Cifeis a vector field, then the divergence of the curt of F must be 0. Od. More than one of the other choices. Oe None of the other choices.

Which of the following statements is incorrect, assuming that all second-order partial derivatives exist and are continuous? Assume that "o* can stand for eithier a scalar or a vector, depending on context. O an fis a scalar function, then the curl of the gradient of f must be 0. O br s is a scalar function, then the divergence of the gradient of / must be 0. O Cifeis a vector field, then the divergence of the curt of F must be 0. Od. More than one of the other choices. Oe None of the other choices.

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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QUESTION 3 Which of the following statements is incorrect, assuming that all second-order partial derivatives exist and are continuous? Assume that "o" can stand for either a scalar or a vector, depending on context. O a. If fis a scalar function, then the curl of the gradient of f must be 0. O b.if f is a scalar function, then the divergence of the gradient of / must be O Cifpis a vector field, then the divergence of the curt of F must be 0. O d. More than one of the other choices. O e. None of the other choices.
Transcribed Image Text:QUESTION 3 Which of the following statements is incorrect, assuming that all second-order partial derivatives exist and are continuous? Assume that "o" can stand for either a scalar or a vector, depending on context. O a. If fis a scalar function, then the curl of the gradient of f must be 0. O b.if f is a scalar function, then the divergence of the gradient of / must be O Cifpis a vector field, then the divergence of the curt of F must be 0. O d. More than one of the other choices. O e. None of the other choices.
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