Find the linearization L(x,y) of the function f(x,y) = 3x - 3y+6 at the points (0,0) and (1,1). The linearization of f(x,y) at (0,0) is The linearization of f(x,y) at (1,1) is

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: Consider the function g(x, y) = x² + xy + y² (1 + 1/2t, 2 + V3/2t), use the (a) Given the line l(t)…

A: Given,              g(x, y)=x2+xy+y2

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at…

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Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: Find the linearizations L(x, y, z) of the function at the given points. ƒ(x, y, z) = xy + yz + xz at…

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Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

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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 linearization L(x, y) of the function ateach point. ƒ(x, y) = x2 + y2 + 1 at a. (0, 0), b.…

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Q: 8 Find the linearization L(x, y) of the function at the given point f(x, y)=1+xIn(xy-5), (2,3)

A: Given: f(x,y)=1+xln(xy−5)(2,3)L(x,y)=?

Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

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Q: Find the linearization L(x,y) of the function f(x,y) = 8x – 7y + 8 at the points (0,0) and (1,1).…

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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 linearization L(x, y) of the function ateach point. ƒ(x, y) = (x + y + 2)2 at a. (0, 0), b.…

A: Given function,  f(x, y) = (x + y + 2) 2 To find linearisation L(x, y) at i) (0, 0)  ii) (1, 2)

Q: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

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 partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

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Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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Q: Find the gradient of the function z = ln(x2 − y) /(x − 4), at the given point     (2, 3)

A: To find the gradient differentiate z partially with  respect to x and y. Given function  z=lnx2-yx-4…

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 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 f(x, y) =x2-5xy+y2 at the point (0, 1)

A: Gradient of the f(x,y) at a point (a,b) is given by :∇f=dfdx(a,b)i+dfdy(a,b)j

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 w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

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Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A: Function: f(x,y,z)=xy+yz+zx, at(0,0,0) We need to find fx,fy,fz. at the point (0,0,0)

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

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: Find the linearization of the function at the given point. f(x y, z) = e5x - 3y - 6z at (0, 0, 0)…

A: Linear approximation in three Variables

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: To find the linearization Lx,y,z of the function at the given points fx,y,z=x2+y2+z2 at 1,0,0

Q: Find the linearization of the function at the given point. f(x,y,z) = 10xy + 7yz+ 9zx at (1,1,1) O…

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Q: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

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Q: Find the gradient of f(x,y,z)=xy+yz+xz at point P(1,2,3).

A: As we know that the expression for the gradient is: ∇fx,y,z=i∂∂x+j∂∂y+k∂∂zfx,y,z Given:…

Q: Find the gradient of the function at the given point. In(x² – y) – 3, (3, 8) z = 1 Vz(3, 8) = 2i

A: I have checked the work. Calculation is correct.

Q: Find the linearizations L(x,y,z) of the function f(x,y,z) = 4xy + yz + 3xz at (1,1,1), (1,0,0), and…

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Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Find the linearization L(x.y) of the function f(x.y) = 2x- 7y + 3 at the points (0,0) and (1,1). The…

A: f(x,y)= 2x-7y+3 fx  = 2 fy = -7 The linearization of a function f(x,y) at (a,b) is given by L(x,y) =…

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: Find the linearization L(x,y) of the function f(x,y) = 2x – 3y + 4 at the points (0,0) and (1,1).…

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

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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…