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Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity.

Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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In this question you'll investigate an infinite 3D shape known as Gabriel's Horn. This shape strangely enough has a FINITE volume but an INFINITE surface area. Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity. 1/4 for x21. x x=( y=( X=27=2 x= 1/2 y=2 P * dx (✗ Tim red area nt Tim + dx = = 11 1 Tim to in 1x1 / 2 Tim Intl - Inl1 +700 I'm In It! ∞ infinite area +700
Transcribed Image Text:In this question you'll investigate an infinite 3D shape known as Gabriel's Horn. This shape strangely enough has a FINITE volume but an INFINITE surface area. Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity. 1/4 for x21. x x=( y=( X=27=2 x= 1/2 y=2 P * dx (✗ Tim red area nt Tim + dx = = 11 1 Tim to in 1x1 / 2 Tim Intl - Inl1 +700 I'm In It! ∞ infinite area +700
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