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
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)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41a1af84-f79e-495e-9bf6-e155c46aa5b8%2Fdff7dd42-f11d-44b4-b378-08b6bd0f7ee6%2Fodem9iq_processed.jpeg&w=3840&q=75)
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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