L₂F F = (4x³z, 4y³z, 3z¹) S is the surface of the solid bounded by the hemispheres 16 — x² - y², z = √√√√4 – x² — y² and the plane Calculate Z= z = 0. F.ds where

Q: Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z =…

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Q: Find the surface area of the portion of the part of the paraboloid z = 7 - 2x² – 2y² that lies above…

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Q: Find an equation of the plane that contains the intersection points of the ellipsoid 9x? + 4y² + 9z²…

A: GIVEN : Ellipsoid 9x2 +4y2 + 9z2 = 36

Q: the surface z = &x + 4y th=

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Q: Find the surface area of the portion of the plane z=6-3x-3y which lies in the 1st octant I)2sqrt18…

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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…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Find the surface area of the part of the paraboloid z=2x² +2y² that lies under the plane 2=16.

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Q: Q5) Find the equation of the surface formed by rotating the following line about the x -axis. 1=…

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Q: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: · ƒ [‚²³ · F . S F = (4x³z, 4y³z, 3z¹) Calculate dS where and S is the surface of the solid bounded…

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Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

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Q: Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the…

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