9. S is the part of the cone surface z = oriented upward (no top). Vx2 + y? that lies under the plane z = 3, Evaluate / (2x + sin(y? + y) + 2°, x² + y + z, y² + 2²) · dS.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: Compute dS where F = (x, Y, z) and S is the surface of the cone z2 = x² + y² for 0 < z < 4 plus its…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of the portion of the cylindrical surface y = 4 – x² in the first octant that is…

A: Find your answer below below

Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

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Q: How would you evaluate [[ F-dS, where S is the surface with param etrization G(4, v) with domain D?

A: We need to demonstrate the method of evaluating the surface integral. ∬SF.dS Where, parametrisation…

Q: ns are pre uestionnaire). Box Luck!!! Question 46 Which of the following best describes the surface…

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Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

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Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: Evaluate the surface integral. x²z² ds S is the part of the cone z² = x2 + y2 that lies between the…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder 22 + y?…

A: We have to find surface area of the plane z=5+4x+3y that lies inside the cylinder x^2+y^2=16.

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

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Q: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

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Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: * Find the surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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Q: If V = (x +y) z, evaluate ∮ ? ??, where S is the surface of the cylindrical wedge defined by 0 < ϕ <…

A: Consider the given information. V=x+yz and the given limits are 0&lt;ϕ&lt;π2, 0&lt;z&lt;2. Convert…

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

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 part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.

A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

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Q: Evaluate the surface integral. x2z2 dS S is the part of the cone z2 = x2 + y2 that lies between the…

A: Given: The surface integral is given as, S is the part of the cone z2-x2 + y2 that lies between the…

Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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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: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

A:

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

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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: Which cylindrical surface below is perpendicular to the yz-plane? O x^2 + y^2 - z^2 = 1 O x = y^2 +…

A: If a cylinder is perpendicular to any plane then it will represent  a circle at a point parallel to…

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

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of…

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Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

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Q: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

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Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Find the surface area of the part of the plane z = 7+ 5x + 3y that lies inside the cylinder 2+ y² =…

A: Surface area: -The definite double integrals determine the surface area of any surface enclosed by a…

Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…

Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Find the surface area of the portion of the semi cone z = x2 + y? that lies between the planes z = 6…

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Q: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

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