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Re: [Phys-l] Zero

The answer is NO. But that is for the "definitive" part of your question. The whole point of L'Hospital's Rule in calculus is to address the issue of two functions going to zero with one of those functions divided by the other. The question becomes one of "who gets to zero first."

For example, the sinc(x) function, which is defined as sinc(x) = sin(x)/x is equal to 1 when x= 0. Thus for x=0 you have the case which you describe:
sin(x)/x = sin(0)/0 = 0/0 and the answer is 1 by L'Hospital's Rule.

The sinc(x) function is very common in optics when calculating diffraction patterns for slits.

In general there is no fixed or "definitive" answer for 0/0, you must know how you have approached that point.

Other functions for 0/0 will reach other values including zero and infinity. In the end, L'Hospital's Rule, rules! :-)

John

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John E. Sohl, Ph.D.
Professor of Physics
Weber State University
2508 University Circle
Ogden, UT 84408-2508

voice: (801) 626-7907, fax: (801) 626-7445
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JMGreen <jmgreen@sisna.com> 10/12/2007 4:19 PM >>>
Has the fraction zero/zero a definitive answer?

Is there a book named "Zero" which purports a definitive answer?

Jim

J M Green
Email: MailTo:JMGreen@sisna.com
WWW: http://users.sisna.com/JMGreen