For each vector field F(x, y, z), compute the curl of F and, if possible, find a function f(x, y, z) so that F = Vƒf. If no such function f exists, enter NONE. (a) Suppose F(x, y, z) = (4yze4xyz +22² cos(xz²))i + (4xze4xyz)j + (4xye¹¹yz + 4xz cos(xz²))k. curl(F) = l f(x, y, z) = i (b) Suppose F(x, y, z) = - + x Y curl(F) = 9. f(x, y, z) = + k (c) Suppose F(x, y, z) = (-3y, 3x, 82). curl(F) = f(x, y, z) =
For each vector field F(x, y, z), compute the curl of F and, if possible, find a function f(x, y, z) so that F = Vƒf. If no such function f exists, enter NONE. (a) Suppose F(x, y, z) = (4yze4xyz +22² cos(xz²))i + (4xze4xyz)j + (4xye¹¹yz + 4xz cos(xz²))k. curl(F) = l f(x, y, z) = i (b) Suppose F(x, y, z) = - + x Y curl(F) = 9. f(x, y, z) = + k (c) Suppose F(x, y, z) = (-3y, 3x, 82). curl(F) = f(x, y, z) =
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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How do i solve the attached calculus question?
Transcribed Image Text:For each vector field F(x, y, z), compute the curl of F and, if possible, find a function f(x, y, z) so that F = V ƒ. If no such function f exists, enter NONE.
(a) Suppose F(x, y, z) = (4yze4xyz + 2z² cos(xz²))i + (4xze¹ryz)j + (4xye4xyz + 4xz cos(xz²))k.
curl(F) =
f(x, y, z) =
(b) Suppose F(x, y, z)
curl(F) =
f(x, y, z) =
i
x
+
Y
+
k
2
(c) Suppose F(x, y, z) = (−3y, 3x, 8z).
curl(F) =
f(x, y, z) =
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