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2. True/False: The vector field G = xi+x*j is not the gradient field of any function g(x, y) w hose second order derivatives are cont inuous over R². (Justify your answer.)

2. True/False: The vector field G = xi+x*j is not the gradient field of any function g(x, y) w hose second order derivatives are cont inuous over R². (Justify your answer.)

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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Please help me answer questions 2 and 3 for this homework. Thanks
1. True/False: The vector fi eld F = yzi + xzj+ xyk is the gradient field of some differentiable function f(x, y, z). (Justify your answer.) 2. True/False: The vector field G = xi + x*j is not the gradient field of any function g(x, y) w hose second order derivatives are cont inuous over R². (Justify your answer.) 3. Find the work of the vector field F(x, y, z) = yi along the curve which is obtained as the intersection of the surfaces z = x2+y? -6 and 6x+12y = z+6. Hint: you may find it useful to complete the squares and use the identity sin? t =}(1 – cos(2t)).
Transcribed Image Text:1. True/False: The vector fi eld F = yzi + xzj+ xyk is the gradient field of some differentiable function f(x, y, z). (Justify your answer.) 2. True/False: The vector field G = xi + x*j is not the gradient field of any function g(x, y) w hose second order derivatives are cont inuous over R². (Justify your answer.) 3. Find the work of the vector field F(x, y, z) = yi along the curve which is obtained as the intersection of the surfaces z = x2+y? -6 and 6x+12y = z+6. Hint: you may find it useful to complete the squares and use the identity sin? t =}(1 – cos(2t)).
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