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A: Topic:-application of algebra
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A: To graph the solution to this system of linear inequalities.y≤12xy>x-5x≤5
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- f(x, 3) In(x2 + Yof function P(3, 4) at the point of = (9, 12) Directional derivative in the direction of the vector to you.Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 1, 1) in the direction of the vector √5 (Use symbolic notation and fractions where needed.) directional derivative: + 2 √5Find the derivative of the vector functionr(t)=ta×(b+tc) wherea=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and c=⟨−3,−2,−3⟩
- Directional derivative of p = 2xz - y2, at the point (1, 3, 2), becomes maximum in the direction of 1. 4i + 2j – 3k 4i — бј + 2k 3. 2i – 6j + 2k 4. 4i - бј - 2k 2.Vector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v = ()i + (_j.Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)
- Calculate the directional derivative of g(x, y, z) = z² - xy + 4y2 in the direction v = (1,-4, 3) at the point P = (3, 1, -9). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(3, 1,-9) =Find the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2,-3, 6) in the direction of the vector v 4i - 3k. %3DFind the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the direction of the vector (- 3, 3)
- Verify the Sum and Product Rules for derivatives of vector-valued functions.Find the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction of the vector 1 2 i+ (Use symbolic notation and fractions where needed.) directional derivative:Calculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect