Let a be a real number and f(x, y) = 3ax?y + 5xy3. Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y). - i) Find Vf(1, 1) in terms of a. ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is -6/5 find a. V2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let a be a real number and f(x, y) = 3ax?y + 5xy3.
Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y).
-
i) Find Vf(1, 1) in terms of a.
ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is
-6/5
find a.
Transcribed Image Text:Let a be a real number and f(x, y) = 3ax?y + 5xy3. Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y). - i) Find Vf(1, 1) in terms of a. ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is -6/5 find a.
О i) (ба + 5) i + (За + 15) ј, i) -2
О) (ба + 5) і + (За + 15) ј, i) -6
О) (ба + 5) і + (За + 15) ј, ii) 6
О ) (ба + 5) i + (За + 15) ј, i) o
О) (За + 5) i + (-ба + 15) ј, i) -2
О)( За + 5) і + (-6а + 15) ј, i) -6
О i) (За + 5) i + (-6а + 15) ј, in) 6
О) (За + 5) i + (-ба + 15) ј, i) 0
Transcribed Image Text:О i) (ба + 5) i + (За + 15) ј, i) -2 О) (ба + 5) і + (За + 15) ј, i) -6 О) (ба + 5) і + (За + 15) ј, ii) 6 О ) (ба + 5) i + (За + 15) ј, i) o О) (За + 5) i + (-ба + 15) ј, i) -2 О)( За + 5) і + (-6а + 15) ј, i) -6 О i) (За + 5) i + (-6а + 15) ј, in) 6 О) (За + 5) i + (-ба + 15) ј, i) 0
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