Consider the following function. f(x, y, z) = √√x² + y² + z² Find f (x, y, z), f(x, y, z), and f₂(x, y, z). f(x, y,z) fy(x, y, z) = f₂(x, y, z)= Find the linear approximation of the function f(x, y, z)=√√√x² + y² + z² at (7, 6, 6). f(x, y, z) = Use the linear approximation to approximate the number 7.022 + 5.992 + 5.972. (Round your answer to four decimal places.) f(7.02, 5.99, 5.97) =

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 8xy

A: Given function is f(x, y) = 5xe8xy

Q: Find f, (x.y) and f, (x,y). Then, find f, (1,-3) and f,(-1,- 2). f(x,y) = - 5xy + 2y +6

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Q: Determine the expression for F(x, y, z) given the function F(x, y, z) = 2x²y = xz² + 3y²z.

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Q: evaluate the function at the given point. f(x,y)=x2+y2, D={(x,y):0<=x<=1, 0<=y<=1}

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Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: Compute Fx, fy, and fz for the function and evaluate them at the indicated points

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Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A: The given function .The aim is to find all values of  and  such that .

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy…

A: To find all values of  such that  simutaneously.

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: Find the linear approximation of the function below at the indicated point. f (x, y, z) = V x² + y²…

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Q: f(x, y) = 6 – V4 - x2 - y2 is

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Q: Find the gradient of the function f(x,y) = √√2x+4y at the point (-2,2). Then sketch the gradient…

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