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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
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.
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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