Find a function f(x, y, z) whose level surface f =1 is the graph of the function g(x, y) = 5x + 3y. f(x, y, z) =?

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

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Q: Describe the level surface F(x, y, z) = 0.…

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Q: Find the absolute minimum and absolute maximum of the function f(x, y) = x^3 – 2y^3 + 3y + (x – 1)^2…

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Q: Find the absolute minimum for the function f(x,y) = 7 +7x² +7y² bounded between x = 3, x = 9, y = 4…

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Q: Sketch a typical level surface for the function. 10) f(x, y, z) = /x2 –z %3D

A: sketch a typical level surface for the following 10) fx,y,z=x2-z it is known that level surface is…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: Find the maximum rate of change of the function f(x, y) 4y at the point (5,1)

A: Given f(x, y) at (5, 1)  We have to find find the maximum rate of f(x, y) at (5, 1) by using the…

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Find the absolute maximum and minimum values of the function f (x, y) = x – y + xy on the closed…

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Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Find the absolute maximum and absolute minimum values of the function f(x, y) 2x3 + 3xy + 2y %3D…

A: We have to find the absolute maximum and absolute minimum values of the function fx,y=2x3+3xy+2y3…

Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 5x + 8y on the…

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Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: sketch a typical level surface for the function. ƒ(x, y, z) = ln (x2 + y2 + z2)

A: The given function is  ƒ(x, y, z) = ln (x2 + y2 + z2). In order to sketch the typical level surface…

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 10 – 2x + 3y osed triangular region with…

A: Given: f(x, y)=10-2x+3yWith vertices (0, 0), (3, 0) and (3, 4)

Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: Find the minimum and maximum values of: f (x, y) = x² + xy bounded by the graphs y = x´ and y =9

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Q: Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region…

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Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: Justify why the level curves very close to the origin (0,0) for the function f(z, y) = (1-z)(1 – )…

A: As per the instruction, we will be solving the first question. For (1), We are given the function as…

Q: st, enter DNE.) f(x, y) = x² + y² + 4x 10y6 minimum maximum point (x, y, z) = (x, y, z) = (x, y, z)…

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Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

A: Minimal distance

Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

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Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: Find an equation for the level surface of the function f(x,y,z) = Vx+ y - Inz through the given…

A: Solve the given

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

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Q: Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and…

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Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 5z) at the point (- 1, 1, 2).

A: We have to find

Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: What is the largest vertical distance between the graphs of the functions y = Vx and y = x² in the…

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Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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