Re: opponents of taylor and l'hospital ?

In article <4VseSEovwEPDM9afsm8KhiLuj141@xxxxxxx>,
"[Mr.] Lynn Kurtz" <kurtz@xxxxxxxxxxxxxxx> wrote:

On Mon, 05 May 2008 00:27:58 GMT, Gerry Myerson
<gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:


There's an objection to using l'Hopital to do
limit as x goes to zero of (sin x) over x.

The objection is that to use l'Hopital, you need
to know
the derivative of sin x --- but to know the
derivative
of sin x, you have to know the limit as x goes to
zero

why do you need the limit as x goes to zero to compute the derivatative of sin x ??

its not that hard ?

1) its very well known
2) you can use taylor series
3) you can use nilpotent numbers h =/= 0 and h ^ 2 = 0


of (sin x) over x, so using l'H is circular (no
pun intended)
reasoning.

I don't recall ever seeing the limit for sin(x)/x
developed in any
calculus book by using L'Hospital's rule. Have you?

well actually i have.

dont remember which one , and it might not have been a good one , but im sure i have.



No, not in any book - but on student papers, yes,
many times.
The objection is really to assigning that limit as a
problem
when you're teaching l'H.

why ? you can use that example to demonstrate l'H.



--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for
email)

regards
tommy1729
.

Relevant Pages

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