c) Given a function $(x, y, 2) = 3x² + In (3y² + 1) + e* cos z. i. Find the directional derivative of ø at (0, 1, 7) in the direction of a = 4i – 2j + 4k. ii. Find the minimum directional derivatıve or ø and its uirection at (0, 1, 7).

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

Q: B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the…

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Q: 2 Suppose that A = 3xyz²7 + 2xy³j - x²yzk and p = 3x² - yz. Find, at the point (1,-1, 1), 2.1 Vo,…

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Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

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Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

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Q: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

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Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: II. Consider the function g defined by g(x, y) 3 = cos (Tx /y) + х — у Do as indicated. 1. Determine…

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Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: 1(x, y, z) = ln(2x + 4y + z²), at the point u = (−1,1,0), in the direction of the unit vector…

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Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: The given scalar field is - f(x,y,z)=(x^2)z+(y^3)(z^2)-xyz

Q: Definition 3.27 Let P(x, y) be a point in R² and 0 be the radian measure of the angle formed by OP…

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