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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.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 8AEXP
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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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