Given: F(x, y, z) = e²² + sin(4x + 6y − 2) - - x ln(2y - 3) 3 and P(-3,2,0). (a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6). (b) Find the unit vector in the direction where F decreases most rapidly at P. (c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 at P.
Given: F(x, y, z) = e²² + sin(4x + 6y − 2) - - x ln(2y - 3) 3 and P(-3,2,0). (a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6). (b) Find the unit vector in the direction where F decreases most rapidly at P. (c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 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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![Given: F(x, y, z) = e²z + sin(4x+6y-z) -
x ln(2y - 3)
3
and P(-3,2,0).
(a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, -6).
(b) Find the unit vector in the direction where F decreases most rapidly at P.
(c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 at P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58ee7c61-51fd-4363-a540-85cfd5b20d56%2F04f795eb-0a41-438c-ae22-40991266922f%2F1ncawoe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given: F(x, y, z) = e²z + sin(4x+6y-z) -
x ln(2y - 3)
3
and P(-3,2,0).
(a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, -6).
(b) Find the unit vector in the direction where F decreases most rapidly at P.
(c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 at P.
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