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If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T 6 which of the following expressions equals Duf(x, y)

If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T 6 which of the following expressions equals Duf(x, y)

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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If f(x, y) = 2x² + 5₁² and u is the unit vector in the direction of π 6 which of the following expressions equals Du f(x, y) ? lim h→0 lim h→0 lim h→0 2 ²(x + = ₁ ) ² + 5 ( x + √2/²₁ ) ² − (2x² + 58² ) 2x 5y - h None of the given choices lim h→0 2 2 2 ( x + √2/²₁) ²³ + 5(x + √2/² » ) ² − (2x² + 53²) - y - h 2 2 ( x + √/³√n ) ² + 5(x + ²√n) ² - + 5 (y +_h) − (2x² + 5y²) h 2 2 ² ( x − — ^)² + 5 ( x − 4 /³^₁) ³² - (2x² + 55²) √3 2 y h
Transcribed Image Text:If f(x, y) = 2x² + 5₁² and u is the unit vector in the direction of π 6 which of the following expressions equals Du f(x, y) ? lim h→0 lim h→0 lim h→0 2 ²(x + = ₁ ) ² + 5 ( x + √2/²₁ ) ² − (2x² + 58² ) 2x 5y - h None of the given choices lim h→0 2 2 2 ( x + √2/²₁) ²³ + 5(x + √2/² » ) ² − (2x² + 53²) - y - h 2 2 ( x + √/³√n ) ² + 5(x + ²√n) ² - + 5 (y +_h) − (2x² + 5y²) h 2 2 ² ( x − — ^)² + 5 ( x − 4 /³^₁) ³² - (2x² + 55²) √3 2 y h
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