Suppose that over a certain region of space the electrical potential V is given by the following equation. V(х, у, 2) 4x2 — Зху + хуz %3D (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i +j- k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(х, у, 2) 4x2 — Зху + хуz %3D (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i +j- k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?

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

Suppose that over a certain region of space the electrical potential V is given by the following equation.
V(х, у, 2) %3
4x2 - Зху + хуz
(a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i +j- k.
(b) In which direction does V change most rapidly at P?
(c) What is the maximum rate of change at P?

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