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

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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
Transcribed Image Text: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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