Find the area of the surface z = x² + y? that lies below the plane z = 2.

Q: Find the area of the paraboloid x? + y +z² = 2 by the plane y = 0.

A: We need to calculate the area of the paraboloid x2+y+z2=2 that is cut by the plane y=0. The equation…

Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: Find the volume under the paraboloid z-x+y above the triangle enclosed by the lines y=x, x=0 and…

A: Volume is the amount of space occupied by the closed surface. In this problem, we have to calculate…

Q: Find the area of the surface of revolution r(u, v)= 6sin(u)cos(v)i+ 6uj+6sin(u)sin(v)k, where 0SusT…

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

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y?…

A: Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is…

Q: Find the surface area when C {(x, y): 0 ≤ x ≤ 2; y = 1 is revolved about the y-axis.

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 =…

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x? + y2 =…

A: Consider the formula for the Surface and the function f(x,y).Calculate fx and fy by partially…

Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8 that lies inside the cylinder x?…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder a2 + y?…

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Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

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 defined by x + y + z = 1, x2 + 8y2 s 1.

A: Given,            x+y+z=1,     x2+8y2≤1

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: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Find the volume under the paraboloid z = x2 + y2 above the triangle enclosed by the lines y = x, x =…

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Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: Use​ Pappus's theorem for surface area and the fact that the surface area of a sphere of radius a is…

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Q: Find the volume of the solid bounded by the paraboloid z = 2 – 4x? – 4y? and the plane z =

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Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Find the surface area if C = {(x, y): 1 ≤ x ≤ 2,y = about the x-axis.

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Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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Q: f (x, уy) %3D — 3х — 2у + 6 | R = {(x,y) : 0 <x< 2,0< y< 2 – x )}

A: Given query is to find the area bounded by the region.

Q: Find the area of the portion of the surface z=f(x,y) = x^2+ y^2 that lies below the plane z = 9.

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: Find the area of the section of the surface x = u2, y = uv, z = v2/2 bounded by the curves u = 0, u…

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x² + y2 =…

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

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Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: (b) Find the volume under the paraboloid z=x+y² above the triangle enclosed by the lines y=x, x=0…

A: To find the volume of the given solid.

Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Find the area of the part of the surface z = xy that lies within the cylinder x2 + y2 = 9.

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Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

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: Find the surface area of the paraboloid z = x² + y², 0 < z < 1. .

A: The surface is same as revolving the curve x2=z or x=z1/2, y=0 about z- axis. So surface area is:…

Q: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, 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: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

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 ,…