Consider the following 2 1 f(x, у, z) — хе5уг, Р(1, 0, 1), 3' 3 3 (a) Find the gradient of f. VF(x, у, z) (b) Evaluate the gradient at the point P. Vf(1, 0, 1) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 0, 1)

Q: Consider the following. xY,z) = Vx+ yz. Р(1, 3, 1), (a) Find the gradient of f. Vfx, y, z) = (b)…

A: Given that                   f(x,y,z)=x+yz                   P(1,3,1)                  u=(67,27,37)…

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

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Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

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Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of…

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Q: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, –3) Vw(10, 5, –3) =

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Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point. Given is the function  f(x,y)=e5xsin(5y).…

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: Consider the following. FOx, v, 2) = x²yz - xyz", P(4, -1, 1), u =(0,-) (a) Find the gradient of f.…

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Q: Suppose that f(æ, y, z) = x²yz – xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: In this question we will use basic of vector  calculus i.e gradient of any function.  We will first…

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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Q: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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Q: Find the gradient of the function f(r, y, 2) = x In(yz), at the point (-2, 1, e) Vf(-2, 1, e) =

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 8, –3) Vw(9, 8, -3) =

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Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

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Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

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Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: 25 Find the gradient of f(x, y) : at (-2, 1). x² + y? NOTE: Enter the exact answer. grad f =|? i+ ?…

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Q: Find the gradient of the function at the given point. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

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Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

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Q: Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

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Q: Calculate the gradient of f(x, y) xy at (r, y) = (- 3, – 2). %3| V f(– 3, – 2)

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (8,4, –2) Vw(8, 4, -2) =

A: Given problem:- Find the gradient of the function at the given point. w = x tan(y + z) , (8, 4, -2)

Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3) Vw(17, 6, -3) =…

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Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: Consider the level curves for F (x, y) = x² – y². y (a) How do we sketch in the gradient vectors?…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 7, -4) Vw(19, 7, –4) =

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Q: 2. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) Vw(10, 5, -2) =

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Q: Consider the function f(x,y,z) = x2 + 4y2 + 2z2 + 2, the point P(3,0,1), and the unit vector u = 1…

A: As per our guidelines, I can answer only three subparts of a question. To know rest, please re…

Q: Find the gradient of f at the indicated point f(x,y,z)=yz3-2x2; P(2,-3,1)

A: The formula to find the gradient is ∇f=∂fx,y,z∂x,∂fx,y,z∂y,∂fx,y,z∂z, that is partially…

Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: For the function f(x,y, z) := 10r + 7y³ + 723 + 9ry + 6yz+ 12rz+ 19 find the gradient at the point…

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Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: Consider the following. 4 12 3 fix, y, 2) %3D у?ехуг, P(0, 3, -3), и 3 13' 13' 13 (a) Find the…

A: Givenf(x,y,z)=y2exyz P(0,3,-3) ,u = 413,1213,313

Q: Find the gradient of the function at the given point. w - x tan(y + z), (8, 5, –2) Vw(8, 5, –2) =

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Q: Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional…

A: Given: fx,y=x+yy+1 The gradient of fx,y can be calculated as, ∇fx,y=i^∂∂xfx,y+j^∂∂yfx,y Here,…

Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

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Q: Let f(x, y) = x /G. At the point (1, 4), find a vector (a) In the direction of maximum rate of…

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Q: Find the gradient of the function w = 6xy − y2 + 2xyz3, at the given point  (−1,  5, −1)

A: To find the gradient, take the derivative of the function with respect to x,y,z.