Find the directional derivative of f(x, y, z) = zy + x* at the point (2, 1, 3) in the direction of a vector making an angle of *with Vf(2, 1, 3). Consider the vector field F(x, y, z) = (-2y, –2x, 8z). Show that F is a gradient vector field F = VV by determining the function V which satisfies V(0,0,0) = 0.V (т, у, 2) —

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Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a vector making an angle of S with Vf(2,1, 3).

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

Find the directional derivative of f(x, y, z) = zy + x* at the point (2, 1, 3) in the direction of a vector making an angle of *
with Vf(2, 1, 3).

Consider the vector field F(x, y, z) = (-2y, –2x, 8z). Show that F is a gradient vector field F = VV by determining the function V which satisfies V(0,0,0) = 0.
V (т, у, 2) —

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