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Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 4xy + xyz %3! (a) Find the rate of change of the potential at P(4, 4, 6) in the direction of the vector v = i +j -k. 12/3 (b) In which direction does V change most rapidly at P? (52,8,24) (c) What is the maximum rate of change at P? 4V 206

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 4xy + xyz %3! (a) Find the rate of change of the potential at P(4, 4, 6) in the direction of the vector v = i +j -k. 12/3 (b) In which direction does V change most rapidly at P? (52,8,24) (c) What is the maximum rate of change at P? 4V 206

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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Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 4xy + xyz %3! (a) Find the rate of change of the potential at P(4, 4, 6) in the direction of the vector v = i +j- k. 12/3 (b) In which direction does V change most rapidly at P? (52,8,24) (c) What is the maximum rate of change at P? 4/ 206
Transcribed Image Text:Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 4xy + xyz %3! (a) Find the rate of change of the potential at P(4, 4, 6) in the direction of the vector v = i +j- k. 12/3 (b) In which direction does V change most rapidly at P? (52,8,24) (c) What is the maximum rate of change at P? 4/ 206
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