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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 = 2T V1+ x dx 1 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.)

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 = 2T V1+ x dx 1 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.)

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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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 = 2T V1+ x dx 1 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.)
Transcribed Image Text: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 = 2T V1+ x dx 1 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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Given:

    y = 1/x 

  Limit: 1 to infinity 

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