Find the extreme values of f(x,y,z) = xyz + 1 on the intersection of the plane z=3 with the sphere x +y +z = 33. The minimum of f(x,y,z) on the domain is. (Type an exact answer, using radicals as needed.)

Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

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Q: Integrate H(x, y, z) = yz, over the part of the sphere x2 + y2 + z2 = 4 that lies above the cone z =…

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Q: Consider the surfaces  z = x^2 +y^2   and z+ 2x+ 2y = 0 Find the projection of the curve on…

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Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find the area of the surface. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

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Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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Q: Find the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and…

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Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x + 2y and the plane z = 8.…

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

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Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z…

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Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Q– Fin the surface area of the portion of the paraboloid z= 6-2x - y that is above the x-y plane…

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Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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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: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

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Q: Find the area of the surface. The part of the paraboloid z = 1 - x² – y2 that lies above the plane z…

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Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane Z = 8.

A: The main objective is to find the volume of solid that lies between the paraboloid z=2x2+2y2 and the…

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: Find the extreme values of f(x,y,z) = x-yz + 1 on the intersection of the plane z= 3 with the sphere…

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