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Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the -axis. otating f(r) VT around the r-axis.

Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the -axis. otating f(r) VT around the r-axis.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Activity: 1. Compute the area of the surface formed when f(z) 2V1-z between-1 and 0 is rotated around the -axis. 2. Compute the surface area of example 9.10.2 by rotating f(z) V around the z-axis. 3. Compute the area of the surface formed when f(x)= between 1 and 3 is rotated around the z-axis. > 4. Compute the area of the surface formed when f(r) 2+cosh(z) between 0 and 1 is rotated around the x-axis. > 5. Consider the surface obtained by rotating the graph of f(z) 1/2, z 21, around the z-axis. This surface is called Gabriel's horn or Toricelli's trumpet. In exercise 13 in section 9.7 we saw that Gabriel's horn has finite volume. Show that Gabricl's hern has infinite surface %3D area, 6. Consider the circle (r-2) + y 1. Sket ch the surface obtained by rotat ing this circie about the g-axis. (The surface is called a torus.) What is the surface area? >
Transcribed Image Text:Activity: 1. Compute the area of the surface formed when f(z) 2V1-z between-1 and 0 is rotated around the -axis. 2. Compute the surface area of example 9.10.2 by rotating f(z) V around the z-axis. 3. Compute the area of the surface formed when f(x)= between 1 and 3 is rotated around the z-axis. > 4. Compute the area of the surface formed when f(r) 2+cosh(z) between 0 and 1 is rotated around the x-axis. > 5. Consider the surface obtained by rotating the graph of f(z) 1/2, z 21, around the z-axis. This surface is called Gabriel's horn or Toricelli's trumpet. In exercise 13 in section 9.7 we saw that Gabriel's horn has finite volume. Show that Gabricl's hern has infinite surface %3D area, 6. Consider the circle (r-2) + y 1. Sket ch the surface obtained by rotat ing this circie about the g-axis. (The surface is called a torus.) What is the surface area? >
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