The gradient of the functiong(x, y, z) = In a In y In z at the point (2, 4, 3) is:

Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: Find the gradient of F(x,y,z)= (xy^2)lnz

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Q: Calculate the gradient Vf, where f (x, y) = In(x² + y²).

A: Given:- f(x,y)=lnx2+y2 To find:- Gradient of f ∇f

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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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: The gradient of f(x, y) = zy at (z, y) = ( – 2, – 1) is %3D

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (18, 4, –1) Vw(18, 4, -1) =|…

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Q: The gradient of f(æ, y) = e3 * sin(2 · y) at (2, y) = (3, – 2) is defined as followed: V f(æ, y) =…

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

A: option (b) is correct

Q: Find the gradient of the function f(x,y,z)=y^(2)ln(xz), at the point (1,−1,e) ∇f(1,−1,e)=?

A: Given query is to find the gradient of f(x,y,z) at a point (1,-1,e).

Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 1, (1, 3) %3D Vf(1, 3) =

A: ∇f = <∂f/dx, df/dy> ∂f/dx = 4 df/dy = 10 y

Q: Calculate the gradient of h(x, y, z) = x z

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Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: Find the gradient of f(r, y, z) = xy?z³ + In(ryz) at the point (1, 1, 1).

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Q: find the gradients of the functions below a)f (x, y, 2) = ye* + 22 in P(0, 2, :

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i…

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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: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

A:

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vf|(1,2,2) = Oi+Dj+Ok (Type integers or simplified…

A: ∇f(x,y,z) = ∂∂xi+∂∂yj+∂∂zkf(x,y,z)

Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O 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 functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: Compute the gradient Vf of the function f given by f(x, y) + y at an arbitrary point (x, y). Then…

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Q: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

Q: Compute the gradient of each of the following functions. а. f(х, у, 2) %3D х sin(yz) b. f(x, y, z) =…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q h(x,…

A: Use the gradient to find the directional derivative of the function at P in the direction of Q h(x,…

Q: Find the gradient of the function f(x, Y, z) = y² ln(za), at the point (e, –1, 1) Vf(e, –1,1) =

A: The given function fx,y,z=y2ln(zx)

Q: Calculate the gradient of h(x, y, z) = x2 Z

A: Given h(x,y,z)=x1y3z. The objective is to find the gradient of h.

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: The gradient of f(x, y) is defined as Vf(2, y) = fa(x, y) + fy(x, y). %3D

A: We know that,             If f is afunction of two variables x and y , then the gradient of the…

Q: Find the gradient of the function f(x,y, z) = xy°z³ at the point (1,1,1).

A:

Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

A:

Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the gradient of the function f(x,y,z)=y^2ln(xz), at the point (1,2,e) ∇f(1,2,e)=

A: Given f(x,y,z) = y2ln(xz)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: find the work done by the gradient of f(x,y,z) =ze^x+2y^2z along the path from (1,2,4) to (-1,0,5)

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Q: The gradient of f(x, y) = ry at (x, y) = (3, 1) is %3D

A: Explanation and solutions is given below....

Q: Find the gradient of the function z(x, y) at the given point P: z = cos(x² + y²), P(3, — 4).

A: The given function is z=cos(x2+y2), P(3,-4).

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

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Find the gradient of f(x,y,z) = sin x ln y + z^3

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Q: Compute the gradient for the function f (x, y) = 4x² – 9y at the point (10, -9) %3D

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Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

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: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…