Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0) and (0, 1). O 0,74 O 2,22 O 10,00 O 6,67 O 20,00

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Q: Find the maximum value of f(z, y) = 12zy(12 – 60z – 12y) over the triangle with vertices (0,0).…

A: Given function is fx,y=12xy12-60x-12y=144xy-720x2y-144xy2             (i) Differentiating (i)…

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Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

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Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

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Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: Find the maximum value of the function f(x,y,z) = plane x+y + z = 1. x² + y? + z² on the %3D

A: The solution is given below in the next step:

Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2,…

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Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

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Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: Find the linearization L(z, y) of f at the given point. Surface: f(a, y) In(x +9y) Point: (11e5,e)…

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Q: Evaluate F.dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise around the…

A: The objective is to evaluate ∫CF·dr where Fx,y=2y-3cosxi+4x+6sinyj and C goes counterclockwise…

Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

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Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

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Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

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Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: Find the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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