Only #3 1) Use a double integral to find the area of the region enclosed by y= ÷x² and y = 2x.2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrantoutside the circle r= 2 and inside the cardioid r= 2 + 2 cos 0.3) Find the surface area of the portion of the paraboloid z = x² + y² below the plane z = 1.4) Use rectangular coordinates and a triple integral to fine the volume of the solid regionenclosed by z = 5x2 + 5y2 and z = 6 - 7x2 - y?.V9-x2 c9-x2-y²5) Use cylindrical coordinates to evaluate , Sx²dzdydx.6) Use spherical coordinates to evaluate S, Sz SN4-x24-x2-y2z2+ y2 + z?dzdydx.x2

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Answered: 3) Find the surface area of the portion…

Math

Algebra

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

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.4: Polyhedrons And Spheres

Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the...

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Question

Only #3

1) Use a double integral to find the area of the region enclosed by y= ÷x² and y = 2x.
2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant
outside the circle r= 2 and inside the cardioid r= 2 + 2 cos 0.
3) Find the surface area of the portion of the paraboloid z = x² + y² below the plane z = 1.
4) Use rectangular coordinates and a triple integral to fine the volume of the solid region
enclosed by z = 5x2 + 5y2 and z = 6 - 7x2 - y?.
V9-x2 c9-x2-y²
5) Use cylindrical coordinates to evaluate , S
x²dzdydx.
6) Use spherical coordinates to evaluate S, Sz SN
4-x2
4-x2-y2
z2
+ y2 + z?dzdydx.
x2

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