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Re: sin x / x = 1 ?
Posted:
Jul 14, 1999 11:57 PM
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Gerry Myerson <gerry@mpce.mq.edu.au> wrote:
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| Robin Chapman <rjc@maths.ex.ac.uk> wrote:
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| > 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.
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| 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
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