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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 eithier a scalar or a vector, depending on context. Oa.f f is a scalar function, then the curl of the gradient of f must be 0 O b.f f is a scalar function, then the divergence of the gradient of f must be 0. OcHeisa vector field, then the divergence of the curl of F must be 0. Od. More than one of the other choices. O e. None of the other choices.

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 eithier a scalar or a vector, depending on context. Oa.f f is a scalar function, then the curl of the gradient of f must be 0 O b.f f is a scalar function, then the divergence of the gradient of f must be 0. OcHeisa vector field, then the divergence of the curl of F must be 0. Od. More than one of the other choices. O e. None of the other choices.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 10EQ
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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 elther a scalar or a vector, depending on context. O a. If f is 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 f must Ocifeis a vector field, then the divergence of the curl of F must be 0. O d. More than one of the other choices. O e. None of the other choices. QUESTION 4 What is the best description of the surface parametrized as x = 3sinucosv, y= 3sinusinv, z = 3cosu with OSUSTI end osVs2n? O a. A cylinder of radius 3 ObA plane through the point (3.3.3) OCA sphere of radius 3. O d. Haif of a sphere of radius3. O e. None of the other choices. QUESTION 5 What is the best description of the surface parametrized as x=3+u, y=3 - v, z=3+u+2v. with u and y any real numbers? O a. A cylinder of radius 3 O b.A plane through the point (3,.3,3) OCA sphere of radius 3 O d. Half of a sphere of radius 3. 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 elther a scalar or a vector, depending on context. O a. If f is 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 f must Ocifeis a vector field, then the divergence of the curl of F must be 0. O d. More than one of the other choices. O e. None of the other choices. QUESTION 4 What is the best description of the surface parametrized as x = 3sinucosv, y= 3sinusinv, z = 3cosu with OSUSTI end osVs2n? O a. A cylinder of radius 3 ObA plane through the point (3.3.3) OCA sphere of radius 3. O d. Haif of a sphere of radius3. O e. None of the other choices. QUESTION 5 What is the best description of the surface parametrized as x=3+u, y=3 - v, z=3+u+2v. with u and y any real numbers? O a. A cylinder of radius 3 O b.A plane through the point (3,.3,3) OCA sphere of radius 3 O d. Half of a sphere of radius 3. O e. None of the other choices.
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