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

Q: Find the directional derivative of the function f: R2→R,  f (x, y)= xy2 + x2y in the direction of…

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Q: Use the gradient to find the directional derivative of the function                  f(x, y, z) = xy…

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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: Use the local linear approximation of f(x, y, z) = In(xz + y) at (2, -1, 1) to approximate f(1.98,…

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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 the gradient of the function f(x, y, z) = zy?, at the point (0, 1,-1) V f(0,1, –1) =

A: We have to find the gradient of the given function at the required point.

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: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: Let f(x, y) = exy and P(1, 0). Solve for the gradient of f at the point P.

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Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Compute the directional deri vative of the function f(z,y, 2) = zy² + y²9+°% at the point P(4, –2,…

A: Given function is fx,y,z=xy2+y2z3+z3x

Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

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Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: The directional derivative of a function f(x, y, z) = xy² – xz + y² at the point Po (1, –1,0) in the…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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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 gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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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 linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = (sin xy)/z at…

A: Linearization of a function of three variable[say f(x,y,z)] at (a,b,c) is…

Q: find the derivative of f(x, y) = x² + xy at P,(1,2) in the direction of the unit vector u = i+ V2

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Q: Find the gradient vector, Vf, for the function, f(x). f(x, y) = x²y² + ex²y b. f(x,y,z) =x²y*…

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Q: Find the gradient of the function f(x,y,z)=2xe^(y/3)sin(3z). grad f=

A: Given f(x,y,z)=2xe(y/3)sin(3z) We need to find gradient of f(x,y,z)

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: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

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Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

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 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 f(x,y, z) = xy°z³ at the point (1,1,1).

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Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

Q: (b) Find the tangent plane and normal line to f(x, y, z) = x²y+y?z+ z2x at the point (1, – 1, 1).

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Q: For a scalar function f(x, y, z) = x? + 3y2 + 2z?, the gradient at the point P(1, 2, - 1) is

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Q: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

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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 f(r, y, z) = z* In(yx), at the point (e, 1, -2) Vf(e, 1, -2) =

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: Let f(x, y, z) = x² – y? + 2z. Compute the rate of change of f in the direction of the vector (v2,…

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Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

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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 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…