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For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y²; P (7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan (²)

For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y²; P (7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan (²)

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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Directional Derivative and Gradient Vector For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y2; P(7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan NIM
Transcribed Image Text:Directional Derivative and Gradient Vector For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y2; P(7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan NIM
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