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With the results on Gabriel's horn under our belt, we will consider another hornlike object. Let g(x)= 1/x for x21, and for b>1 let D, denote the solid obtained by revolving the graph of g on [1, b] about the x axis. a. Find the volume V, of D, and find lim, Vb- b. Prove that the surface area S, of D, satisfies S, <15 for all b>1. (Hint: First find a reasonable positive number M such that /1 + (g'(x))² M for all x> 1.)

With the results on Gabriel's horn under our belt, we will consider another hornlike object. Let g(x)= 1/x for x21, and for b>1 let D, denote the solid obtained by revolving the graph of g on [1, b] about the x axis. a. Find the volume V, of D, and find lim, Vb- b. Prove that the surface area S, of D, satisfies S, <15 for all b>1. (Hint: First find a reasonable positive number M such that /1 + (g'(x))² M for all x> 1.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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With the results on Gabriel's horn under our belt, we will consider another hornlike object. Let g(x)= 1/x for x21, and for b>1 let D, denote the solid obtained by revolving the graph of g on [1, b] about the x axis. a. Find the volume V, of D, and find lim, Vb- b. Prove that the surface area S, of D, satisfies S, <15 for all b>1. (Hint: First find a reasonable positive number M such that /1 + (g'(x))² M for all x> 1.)
Transcribed Image Text:With the results on Gabriel's horn under our belt, we will consider another hornlike object. Let g(x)= 1/x for x21, and for b>1 let D, denote the solid obtained by revolving the graph of g on [1, b] about the x axis. a. Find the volume V, of D, and find lim, Vb- b. Prove that the surface area S, of D, satisfies S, <15 for all b>1. (Hint: First find a reasonable positive number M such that /1 + (g'(x))² M for all x> 1.)
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