sin x / x tends to 1...
- From: Darren J Wilkinson <d.j.wilkinson@xxxxxxxxx>
- Date: Sat, 3 Sep 2005 13:22:46 +0000 (UTC)
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,
--
Dr Darren Wilkinson
mailto:d.j.wilkinson@xxxxxxxxxxxxxxx
http://www.staff.ncl.ac.uk/d.j.wilkinson/
.
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