3) The solid S obtained by rotating the region below the graph of y = x about the x-axis for 1 < x <∞ is called Gabriel's Horn (Figure 11). y =x FIGURE 11 (a) Use the Disk Method (Section 6.3) to compute the volume of S. (Note that the volume is finite even though S is an infinite region.) (b) It can be shown that the surface area of S is A = 27 | aV1+x¯4 dæ Show that A is infinite. (If S were a container, you could fill its interior with a finite amount of paint, but you could not paint its surface with a fınite amount of paint.)
3) The solid S obtained by rotating the region below the graph of y = x about the x-axis for 1 < x <∞ is called Gabriel's Horn (Figure 11). y =x FIGURE 11 (a) Use the Disk Method (Section 6.3) to compute the volume of S. (Note that the volume is finite even though S is an infinite region.) (b) It can be shown that the surface area of S is A = 27 | aV1+x¯4 dæ Show that A is infinite. (If S were a container, you could fill its interior with a finite amount of paint, but you could not paint its surface with a fınite amount of paint.)
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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Transcribed Image Text:3) The solid S obtained by rotating the region below the graph of y = x
Gabriel's Horn (Figure 11).
about the x-axis for 1 < x <∞ is called
FIGURE 11
(a) Use the Disk Method (Section 6.3) to compute the volume of S.
(Note that the volume is finite even though S is an infinite region.)
(b) It can be shown that the surface area of S is
-1
-4
A = 27
x'V1+ x
da
Show that A is infinite.
(If S were a container, you could fill its interior with a finite amount of paint, but you could not paint its surface with a
finite amount of paint.)
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