Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3). (d) Use your answer to part (c) to approximate the value of f(2.02, –3.01) by hand.

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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

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

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Q: Find the linearization of f(x) = xm around r = e. Round the gradient and y-intercept, whenever…

A: First we have to find derivative of the given function.

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

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

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Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: Find the linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the…

A: Given that  f(x,y,z)=√(x^2+y^2+z^2) To find the linear approximation of f(x,y,z) and also find the…

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

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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 the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x y f(x,y) = at (1,2) 1…

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Q: Find the linear approximation to the equation f(, y) = 3. xy at the point (6, 4, 6), and use it to…

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Q: Find the linearization L(x, y) of the function f(x, y) = V161 – læ2 – 16y² at (-4, –3). L(x, y) = ||…

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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 of the function f (z) =23 at z = 1. L(z) = Using this linearlization, f…

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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 linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: f(x. y.z) = + xy + yz + Q8) Find the Linearization at (1,1.2)

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

A: We have to find the gradient of the function  f(x, y) = 2x+4y2+8  at the point (2, 1).

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 orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

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: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

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

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Q: y? = = CX Find the orthogonal trajectories of x2 +

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Q: Use the Chain Rule to calculate dt (r(e)). f(x, y) = 3x – 2y, r(t) = (t°, t°), t = 2 (2, 8), t = 2

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Q: Consider the function f(x, y) = 3x? + ry + 2y? Use the linearization of f(x, y) about (1, 1) to…

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

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Q: Find the Orthogonal Trajectories: a.) y6 = C (x2 + 1)

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Q: For the function: f (x, y) = In(x + 2y) + Find the linearization L(x, y) of the function at the…

A: According to the given information, consider the given function.

Q: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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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 of f(x,y) at the indicated point (Xo,Yo). f(x,y) = /x +2y; (4,7) L(x,y) =

A: Given:- f(x, y) =√x+2y To find:- linearization of f(x,y) at the indicated point (xo.Yo). f(x,y)=√√x…

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

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 linearization of √ x at a = 49. Then use your linearization to approximate √ 56.

A: I am going to solve the given problem by using some simple calculus  get the required result.