Let a be a real number and f(x, y) = 3ax?y + 8xy³. 3i – j and let Vf(æ, y) denote the gradient of f(r, y). Let v = i) Find Vf(1, 1) in terms of a. - 12/5 in) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a. Türkçe: a bir reel sayı olmak üzere f(x, y) = 3ax?y + 8xy³ şeklinde tanımlansın. v = 3i – j ve Vf(x, y), f(x, y) fonksiyonunun gradyanı olsun. i) Vf(1, 1) değerini a değişkeninine göre ifade ediniz. i) f(x, y) fonksiyonunun (1, 1) noktasında v yönünde değişim oranın hızı –12 /5 ise a değerini bulunuz. V2 ) (ба + 8) і + (За + 24) ј, i) -4 i) (ба + 8) і + (3а + 24) ј, iї) -12 ) (ба + 8) і + (3а + 24) ј, iї) 12 ) (ба + 8) і + (За + 24) ј, ij) 0 ) (За + 8) і + (-ба + 24) ј, in) -4 ) (За + 8) і + (-ба + 24) jј, iї) -12 i) (3a + 8) i + (-6a + 24) j, ii) 12 ) (За + 8) і + (-ба + 24) ј, in) 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let a be a real number and f(x, y) = 3ax?y + 8xy³.
3i – j and let Vf(æ, y) denote the gradient of f(r, y).
Let v =
i) Find Vf(1, 1) in terms of a.
- 12/5
in) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is
V2
find a.
Türkçe:
a bir reel sayı olmak üzere f(x, y) = 3ax?y + 8xy³ şeklinde tanımlansın.
v = 3i – j ve Vf(x, y), f(x, y) fonksiyonunun gradyanı olsun.
i) Vf(1, 1) değerini a değişkeninine göre ifade ediniz.
i) f(x, y) fonksiyonunun (1, 1) noktasında v yönünde değişim oranın hızı
–12 /5
ise a değerini bulunuz.
V2
) (ба + 8) і + (За + 24) ј, i) -4
i) (ба + 8) і + (3а + 24) ј, iї) -12
) (ба + 8) і + (3а + 24) ј, iї) 12
) (ба + 8) і + (За + 24) ј, ij) 0
) (За + 8) і + (-ба + 24) ј, in) -4
) (За + 8) і + (-ба + 24) jј, iї) -12
i) (3a + 8) i + (-6a + 24) j, ii) 12
) (За + 8) і + (-ба + 24) ј, in) 0
Transcribed Image Text:Let a be a real number and f(x, y) = 3ax?y + 8xy³. 3i – j and let Vf(æ, y) denote the gradient of f(r, y). Let v = i) Find Vf(1, 1) in terms of a. - 12/5 in) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a. Türkçe: a bir reel sayı olmak üzere f(x, y) = 3ax?y + 8xy³ şeklinde tanımlansın. v = 3i – j ve Vf(x, y), f(x, y) fonksiyonunun gradyanı olsun. i) Vf(1, 1) değerini a değişkeninine göre ifade ediniz. i) f(x, y) fonksiyonunun (1, 1) noktasında v yönünde değişim oranın hızı –12 /5 ise a değerini bulunuz. V2 ) (ба + 8) і + (За + 24) ј, i) -4 i) (ба + 8) і + (3а + 24) ј, iї) -12 ) (ба + 8) і + (3а + 24) ј, iї) 12 ) (ба + 8) і + (За + 24) ј, ij) 0 ) (За + 8) і + (-ба + 24) ј, in) -4 ) (За + 8) і + (-ба + 24) jј, iї) -12 i) (3a + 8) i + (-6a + 24) j, ii) 12 ) (За + 8) і + (-ба + 24) ј, in) 0
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