Let f(x, y) = (x³y², x²y). Obtain a linear approximation of f(x, y) at the point (-1,1) and use this to approximate f(-1.01, 1.02).

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

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Q: Consider choosing x and y to maximise -x-3y, while 1 3y In(3x) + In 3 3 cannot fall below 1.4. What…

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Q: Consider the function - f(x, y) = 2x² + xy² − 6xy + 5x +2. (a) Show that (1,3) is a stationary point…

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Q: f(x, y) = 8 – + xy. I y

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Q: Find fzzz for f(x, y) = x²y².

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Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: F(x,y)=xy+3 find and sketch the domain

A: our objective is to find and sketch the domain of  F(x,y)=xy+3.

Q: Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It…

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Q: Find the analytic function if the imaginary part is (2xy + 5y) where u (0,0) = 0

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Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

Q: Draw the level curve for z = f(x, y) for each of the values listed below. Label each level curve…

A: Equating 2x2-y = z Equating with the values of z we can draw the graph for each function

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Find the linearization of the function f (x) = a° at a = 1.

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Find all stationary points of the function f (x, y) = (x² + y²)² – 2(x² – y²) + 1. | Determine the…

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Q: X+Z+3Siny X +2y-2

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Q: Determine the numerical value of F (2, 3, -1) given the function F(x, y, z) = 2x²y = xz² + 3y²z. y

A: The given function is ; F(x,y,z)=2x2y-xz2+3y2z.

Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.