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Let w = F(x, y, z) = -x² tan(yz) + e²+¹ ln(xy). Let P be the point (1, e, 0). (a) Find the rate of change of F at P in the direction of (-2, 1, 2). (b) What is the maximum rate of change of F at P? (c) If x s² - to find - θω əs t, y = s + 2t² and z = sin(t), use the chain rule when (s, t) = (1,0).

Let w = F(x, y, z) = -x² tan(yz) + e²+¹ ln(xy). Let P be the point (1, e, 0). (a) Find the rate of change of F at P in the direction of (-2, 1, 2). (b) What is the maximum rate of change of F at P? (c) If x s² - to find - θω əs t, y = s + 2t² and z = sin(t), use the chain rule when (s, t) = (1,0).

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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Let w= F(x, y, z) = x² tan(yz) + e²+¹ ln(xy). Let P be the point (1, e, 0). (a) Find the rate of change of F at P in the direction of (-2, 1, 2). (b) What is the maximum rate of change of F at P? (c) If x = s² - t, y = s + 2t² and z = sin(t), use the chain rule δω to find when (s, t) = (1,0). Əs
Transcribed Image Text:Let w= F(x, y, z) = x² tan(yz) + e²+¹ ln(xy). Let P be the point (1, e, 0). (a) Find the rate of change of F at P in the direction of (-2, 1, 2). (b) What is the maximum rate of change of F at P? (c) If x = s² - t, y = s + 2t² and z = sin(t), use the chain rule δω to find when (s, t) = (1,0). Əs
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