Find the linear approximation of the function f(x, y, z) =  sqrt x2 + y2 + z2 at (6, 6, 7) and use it to approximate the number  sqrt 6.022 + 5.992 + 6.972. (Round your answer to five decimal places.) f(6.02, 5.99, 6.97) ≈

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A: Formula Gradient of function f(x,y) ∇f(x,y) = fx(x,y)i + fy(x,y)j Where  fx is partial derivative…

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A: Given that  f(x,y)=x^2/(y^2+1) From the linear approximation to find the f(4.04,0.94)

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A: brief explanation is given below.

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Q: Find the linear approximation of the function f(x, y, z) =    x2 + y2 + z2 at (4, 8, 8) and use it…

A: Solution is given below:

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Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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A: Near 0,

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A: SOLUTION-

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A: For the solution follow the next step.

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = In(x – 4y) at…

A: For the detailed solution of the problem follow the next steps.

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Q: Find the linear approximation of the function f(x, y, z) = V x² + y² + z² at (3, 6, 2) and use it to…

A: Given: f(x,y,z)=x2+y2+z2 at (3,6,2)find f(3.01,5.98,1.97)=3.012+5.982+1.972

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Q: use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z)…

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A: We have to find

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A: linearization of f(x,y) at (a,b) isL(x,y)=f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)....(1)

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A: on solving this we get

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.