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

In article <iqjjh15khq9acibhniar7vqvai1lejkp4b@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:
>On Sat, 3 Sep 2005 13:22:46 +0000 (UTC), 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,

>power series

Stop working so hard; this precedes power series, and
besides, how do you know the power series for sin?

The area of a sector of a circle is between the area
obtained when the endpoint of one point on the circle
is perpendicularly projected on the other side and
the area when the tangent meets the other side extended.

As the ratio of these approaches one, voila!
--
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
.

Relevant Pages

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