Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9 and the coordinate planes.

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the…

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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: X+ 3y and the planes Enclosed by the paraboloid z x= 0, y= 1, y = x, z = 0 13D

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

Q: Let S be the portion of the surface x -2x + y² + z² = 8 for 1<z<2. Find the area of the surface S.

A: x2-2x +y2+z2 =8 ⇒(x-1)2+(y)2+(z)2=(3)2 So the surface S is a circular patch of a circle canter at…

Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

Q: Verdy s Tokes Theorem To F=メー2X54k half-ellipsoid * on any eand Z 70

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Q: Sį : -8(y – 2) = (x – 1)² S2 : y + z = 2 S3 : x = 0 S4 : y = 0 S3 : z = 0 %3D

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Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

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Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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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: Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is…

A: Given surfaces are z=2xyx2+1, z=x+2y  and are bounded by planes x=0 , x=2 , x=-1 , y=0 , y=4. To…

Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: What is the surface area of a hyperbolic paraboloid described by parametric eqn: z = xy, where x,…

A: The surface area of a hyperbolic paraboloid described by the parametric equation z = xy, where x = u…

Q: Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the cone z = x² +…

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Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

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: Closest point is (If there is more than one point, enter a comma-separated list.)

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

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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