Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y) =

Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

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Q: Find the gradient of the function at the given point.

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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: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

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

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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 linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

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Q: Find the orthogonal trajectories of Vy= = CX

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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: 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 direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

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: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

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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: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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

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Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

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) = xy at (x, y) = (3, 1) is

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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 f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

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: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

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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: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

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

Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

A: Linearization of the function f(x,y,z) at (a, b, c) is given by…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

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Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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