Let a be a real number and f(x, y) = 4ax?y + 8xy³. 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. - 12/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is find a. Türkçe: a bir reel sayı olmak üzere f(x, y) = 4ax?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 i) (8a + 8) i + (4a + 24) j, ii) -3 i) (8a + 8) i + (4a + 24) j, ii) -9 O i) (8a + 8) i + (4a + 24) j, i) 9 O i) (8a + 8) i + (4a + 24) j, ii) 0 O i) (4a + 8) i + (-8a + 24) j, ii) -3 O i) (4a + 8) i + (-8a + 24) j, ii) -9 O i) (4a + 8) i + (-8a + 24) j, ii) 9 O i) (4a + 8) i + (-8a + 24) j, ii) 0
Let a be a real number and f(x, y) = 4ax?y + 8xy³. 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. - 12/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is find a. Türkçe: a bir reel sayı olmak üzere f(x, y) = 4ax?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 i) (8a + 8) i + (4a + 24) j, ii) -3 i) (8a + 8) i + (4a + 24) j, ii) -9 O i) (8a + 8) i + (4a + 24) j, i) 9 O i) (8a + 8) i + (4a + 24) j, ii) 0 O i) (4a + 8) i + (-8a + 24) j, ii) -3 O i) (4a + 8) i + (-8a + 24) j, ii) -9 O i) (4a + 8) i + (-8a + 24) j, ii) 9 O i) (4a + 8) i + (-8a + 24) j, ii) 0
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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