Re: sin x / x tends to 1...
- From: "G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 03 Sep 2005 10:18:42 -0400
In article <dfc836$ou0$1@xxxxxxxxxxxxxxxxx>, Darren J Wilkinson
<d.j.wilkinson@xxxxxxxxx> wrote:
> I've a question about the limit of sin x / x as x tends to zero. Of
> course, it's 1 (I think), but I've never seen a satisfactory proof. The
> proof I was given, and the proofs I can find in standard texts all rely
> on knowing the area of a circular sector. However, to know the area of a
> circular sector, one must know the area of a circle. All the derivations
> I know for the area of a circle make use (either directly or indirectly)
> on the sin x / x limit, and there lies my disatisfaction. Of course it's
> easy to get the upper bound of one, and I'm happy to use the area
> argument to establish the existance of a limit. However, it seems to be
> surprisingly awkward to establish the obvious lower bounds (such as cos
> x) using elementary arguments. Does anyone know a nice proof?
>
> Regards,
Classical Greek geometry has a computation of the area of a circle. No
trig involved.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.
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