Let a be a real number and f(x, y) = 2ax²y + 5æy³. Let v = 3i – jand let Vf(x, y) denote the gradient of f(x, y). i) Find Vf(1, 1) in terms of a.
Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).
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A: option (b) is correct
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A: Since solve the first question for you. If youwant any specific question to be solved then please…
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A: We will solve the problem.
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Q: Let a be a real number and f(x, y) = 2ax²y + 8xy³. Let v = 3i – j and let Vf(x, y) denote the…
A: use the formula for gradient of a function.
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A: Please see the answer in step 2
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- Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vectorFind the gradient of the function w = 2x²y – 4yz + z? at the point (1, 1, -2). O 2i+ 10j - 8k O 4i+ 10j- 6k O 2i+ 18j- 6k O 4i+ 10j- Sk O 6i- 14j- 8kLet a be a real number and f(x, y) = 2ax²y + 3xy. Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y). i) Find V f(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 -4/5 find a. v2
- Let a be a real number and f(x, y) = 4ax²y + 8ry³. 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 i) 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) = 4ar?y + 8xy³ şeklinde tanımlansın. v = 3i – j ve Vf(x,y), f(x, y) fonksiyonunun gradyanı olsun. i) V f(1,1) değerini a değişkeninine göre ifade ediniz. ii) f(x, y) fonksiyonunun (1, 1) noktasında v yönünde değişim oranın hızı - 12/5 ise a değerini bulunuz. V2Choose the gradient of f(x, y) = x²y³. (a) 2xi + 3y²j, (b) (c) 2xy³i+3x²y²j, (d) x²i+y³j, y³i+x²j.Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x, y) = 3x2 - y² + 4, P(7,7), Q(8, 4)
- 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) 0Let a be a real number and f(x, y) = 3ax?y + 8xy. 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. -6/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is find a. V2 Türkçe: a bir reel sayı olmak üzere f(x, y) = 3ax?y + 8ry şeklinde tanımlansın. v = 3i – j ve Vf(r, y), f(x, y) fonksiyonunun gradyanı olsun. i) Vf(1, 1) değerini a değişkeninine göre ifade ediniz. ii) f(x, y) fonksiyonunun (1, 1) noktasında v yönünde değişim oranın hızı -6/5 ise a değerini bulunuz. V2 O i) (6a + 8) i + (3a + 24) j, ii) -2 O i) (6a + 8) i + (3a + 24) j, ii) -6 О) (ба + 8) і + (За + 24) ј, in) 6 О) (ба + 8) і + (За + 24) ј. i) 0 O ) (3a + 8) i + (-6a + 24) j, ii) -2 О )(За + 8) і + (-ба + 24) ј, i) -6 о0 (За + 8) i + (-ба + 24) ј, i) 6 O i) (3a + 8) i + (-6a + 24) j, ii) 0a. What is the gradient at the point (4,0,1)?
- Let a be a real number and f(x, y) = 2ar?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(r, y) at the point (1, 1) in the -8/5 direction of v is find a. V2Let v = = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of v.