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Topic: sin x / x = 1 ?
Replies: 54   Last Post: Jul 14, 1999 11:57 PM

 Messages: [ Previous | Next ]
 Bill Dubuque Posts: 156 Registered: 12/6/04
Re: sin x / x = 1 ?
Posted: Jul 14, 1999 11:57 PM

Gerry Myerson <gerry@mpce.mq.edu.au> wrote:
|
| Robin Chapman <rjc@maths.ex.ac.uk> wrote:
| >
| > My objection to L'Hopital is mainly pedagogical. I've found that
| > students immediately latch on to this rule, and will try to use
| > it in *every* situation. It's depressing to see them fill three sides
| > of A4 with a L'H rule that needs to be iterated a few lines when
| > say, a series expansion will do it in two lines.
|
| I find it even more depressing to see them "use" L'H to evaluate
| limit as x -> 0 of (cos x)/x.

An interesting L'Hospital pitfall is the following erroneous deduction

(1 - f) g 1 - f
if g -> 1 then --------- -> ----- -> 1
1 - f g 1 - f

especially when f and g are (truncations of) certain power series.

See my prior post [1] for more on this topic.

-Bill Dubuque

[1] http://forum.swarthmore.edu/epigone/sci.math/shennolfrox/y8zoh31mfmc.fsf@nestle.ai.mit.edu

Date Subject Author
6/24/99 Ren Preston
6/24/99 Gerry Myerson
6/24/99 John Prussing
6/24/99 Nat Silver
6/25/99 David Kastrup
6/29/99 Ren Preston
6/30/99 Erik Max Francis
6/30/99 Virgil Hancher
6/30/99 randy
6/30/99 Robin Chapman
7/1/99 randy
7/2/99 Ronald Bruck
7/2/99 Robin Chapman
7/5/99 Gerry Myerson
6/24/99 Nat Silver
6/25/99 Robin Chapman
6/25/99 Michael Matzl
6/25/99 Robin Chapman
6/25/99 Robin Chapman
6/25/99 Nat Silver
6/25/99 Robin Chapman
6/25/99 Nat Silver
6/27/99 Susan Schwartz Wildstrom
6/27/99 steiner
6/27/99 Michael A. Roche
6/27/99 Ronald Bruck
6/27/99 Michael A. Roche
6/27/99 Ronald Bruck
6/25/99 David C. Ullrich
6/24/99 Ayan Mahalanobis
6/25/99 Ren Preston
6/25/99 Ren Preston
6/25/99 Ingrid Voigt
6/25/99 JZS
6/24/99 Virgil Hancher
6/25/99 JZS
6/25/99 John Savard
6/25/99 Zdislav V. Kovarik
6/30/99 Ren Preston
6/30/99 John Prussing
7/1/99 Virgil Hancher
6/25/99 Jeremy Boden
6/25/99 John Prussing
6/25/99 Nat Silver
6/26/99 John Prussing
6/28/99 Charles H. Giffen
6/27/99 Ronald Bruck
6/27/99 carel
6/27/99 Michael A. Roche
6/27/99 Nikos Mavroyanopoulos
6/27/99 Ayan Mahalanobis
6/27/99 Jeremy Boden
7/5/99 jorge_mascarenhas@my-deja.com
7/14/99 Bill Dubuque