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Suppose the semicircle shown to the right is revolved about the x-axis to generate a sphere. Let AB be an arcy=√√²-x² of the semicircle that lies above an interval of length h on the x-axis. Show that the area swept out does not depend on the location of the interval. Therefore, it does not depend on the location of the slice. Find dy ds, and dx 2 2 the surface area generated by the curve y = √²-x² a≤x≤a+h, about the x-axis. A B a a+h h

Suppose the semicircle shown to the right is revolved about the x-axis to generate a sphere. Let AB be an arcy=√√²-x² of the semicircle that lies above an interval of length h on the x-axis. Show that the area swept out does not depend on the location of the interval. Therefore, it does not depend on the location of the slice. Find dy ds, and dx 2 2 the surface area generated by the curve y = √²-x² a≤x≤a+h, about the x-axis. A B a a+h h

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose the semicircle shown to the right is revolved about the x-axis to generate a sphere. Let AB be an arcy=√²-x² of the semicircle that lies above an interval of length h on the x-axis. Show that the area swept out does not depend on the location of the interval. Therefore, it does dy not depend on the location of the slice. Find ds, and dx 2 the surface area generated by the curve y = √²-x², a≤x≤a+h, about the x-axis. || A B A 0 a a+h प/-
Transcribed Image Text:Suppose the semicircle shown to the right is revolved about the x-axis to generate a sphere. Let AB be an arcy=√²-x² of the semicircle that lies above an interval of length h on the x-axis. Show that the area swept out does not depend on the location of the interval. Therefore, it does dy not depend on the location of the slice. Find ds, and dx 2 the surface area generated by the curve y = √²-x², a≤x≤a+h, about the x-axis. || A B A 0 a a+h प/-
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