(p957, #33) Suppose that over a certain region of space the electrical potential V is given by: V(x, y, z) = 5x² - 3xy + xyz a) Find the rate of change of the potential at P(3, 4, 5) in the direction of the vector v = i+j- k. b) In which direction does V change most rapidly at P? (Express the direction using a unit vector) 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
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Suppose that over a certain region of space the electrical potential ? is given by: ?(?,?,?)=5?^2−3??+???

a)Findthe rate of change of the potential at ?(3,4,5)in the direction of the vector ?=?+?−?.

b)In which direction does ?change most rapidly at ?? (Express the direction using a unit vector)

c)What is the maximum rate of change at ??

(p957, #33) Suppose that over a certain region of space the electrical potential V is given by:
V(x, y, z) = 5x² – 3xy + xyz
a) Find the rate of change of the potential at P(3, 4, 5) in the direction of the vector v = i+j-k.
b) In which direction does V change most rapidly at P? (Express the direction using a unit vector)
c) What is the maximum rate of change at P?
Transcribed Image Text:(p957, #33) Suppose that over a certain region of space the electrical potential V is given by: V(x, y, z) = 5x² – 3xy + xyz a) Find the rate of change of the potential at P(3, 4, 5) in the direction of the vector v = i+j-k. b) In which direction does V change most rapidly at P? (Express the direction using a unit vector) c) What is the maximum rate of change at P?
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