Subject: Re: gabriel's horn
From: George Yanos (gyanos@uic.edu)
Date: Wed Feb 23 2000 - 11:41:18 EST
I hadn't thought of it before you asked, so before you spread this to
your students, think about it for a while: The area under a section of
the curve, and the surface of the trumpet, are both linealry related to
1/x as you move the section to the right. The volume of a corresponding
section of the trumpet, however, is linearly related to (1/x)^2 as you
move to the right.
On Wed, 23 Feb 2000 detzwile@uwc.edu wrote:
>anyone know of a (sort-of) intuitive explanation of the features of
>gabriel's horn?
>
>y = 1/x over zero to infinity
>
>1. area is unbounded; goes to infinity
>2. volume of solid of rev is bounded; approaches pi
>3. surface area of solid of rev is unbounded; goes to infinity
>
>thanks
>
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George Yanos
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708-848-4221(h)
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