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If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T which of the following expressions equals Duf(x, y) " ? lim h-0 lim h→0 lim h→0 2 2(x + 1 h) ² + 5 ( x + √³/h) ² - √√3 2 h O None of the given choices lim h→0 - (2x² + 5y²) 2 2 2 ( x + √² ₁ ) ² + 5 ( x + √ ² ₁ ) ² - h 2 2 h 2 2 ( x + √/²³ ) ² + 5 (v + 1² h) ² - h 5y 2 h (2x² -5y²) - (2x² + 5y²) 2 2(x - ²/ h)²³ + 5 (y - √/³/h) ² - (2x² + 5y²) 2 h

If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T which of the following expressions equals Duf(x, y) " ? lim h-0 lim h→0 lim h→0 2 2(x + 1 h) ² + 5 ( x + √³/h) ² - √√3 2 h O None of the given choices lim h→0 - (2x² + 5y²) 2 2 2 ( x + √² ₁ ) ² + 5 ( x + √ ² ₁ ) ² - h 2 2 h 2 2 ( x + √/²³ ) ² + 5 (v + 1² h) ² - h 5y 2 h (2x² -5y²) - (2x² + 5y²) 2 2(x - ²/ h)²³ + 5 (y - √/³/h) ² - (2x² + 5y²) 2 h

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 4 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) ? lim h→0 lim h→0 lim h→0 2 ( x + = ₁ ) ² + 5 ( x + √2/²^₁)² = (2x² + 5x²) 5y - h None of the given choices lim h→0 2(x + √²2₁) ² + 5 ( x + √2/²₁) ² - (2x² + 53²) 5y h 2 2 2(x + ²)² + 5(x + b)² = (2x² +59²) ₂h) h) √3 (y - h 2 2 √3 2 ( x − 4 ) ² + 5 ( x − +/²₁) ² - (2x² + 55²) 1 y h
Transcribed Image Text:If 4 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) ? lim h→0 lim h→0 lim h→0 2 ( x + = ₁ ) ² + 5 ( x + √2/²^₁)² = (2x² + 5x²) 5y - h None of the given choices lim h→0 2(x + √²2₁) ² + 5 ( x + √2/²₁) ² - (2x² + 53²) 5y h 2 2 2(x + ²)² + 5(x + b)² = (2x² +59²) ₂h) h) √3 (y - h 2 2 √3 2 ( x − 4 ) ² + 5 ( x − +/²₁) ² - (2x² + 55²) 1 y h
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