Re: sin x / x tends to 1...

In article <uSZSe.12282$qY1.529@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
N. Silver <mathelp@xxxxxxxxxxxxxxxx> wrote:
>Liviu wrote:

>> Using variations of your diagram, one can show sin(x) < x < tan(x) which
>> would imply the limit as a corollary. But if you work in terms of areas,

>How do you know that the area of a sector of a
>circle is well-defined? How do you derive a formula
>for area of a sector?

One can get polygons inscribed and circumscribed
whose areas are arbitrarily close. This is enough
to get the area, and in fact was how the Greeks
essentially defined it, using the simple intuitive
properties of measure.

It is likewise clear that the area of a sector is
proportional to the angle.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.