Evaluate the limit of the function f defined by f(x, y) = y = x² as (x, y) approaches (0,0). x+y 2x² + y² along the curve

Q: Find the local extreme values of the function: f(x,y)=xy-x^2-y^2-3x-3y+12.

A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

A:

Q: The level curves of the function f (x, y) = /2x² + y² – 1 are

A: Explanation of the answer is as follows

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A: Given f(x,y)=y8+2x6+2xy For finding fx differentiate f(x,y) with respect to x fy differentiate…

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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Q: Find fyx for f(x,y)=exln(y)

A: Given : fx,y = exlny

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: Find an sketch the domain of f(x,y)= 16x² – x² –4y². -

A: Given that fx,y=16x2-x2-4y2 To determine the domain of the function. fx,y is only defined for…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

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

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Q: 1. (a) Find the domain and range of f. (b) Draw a contour map of f for k=-1,0,1. (c) Sketch the…

A: (a) For the given function, f(x,y)=y+x+2, Assume f(x,y)=z; Here,  z=y+x+2 The domain of z has all…