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


"N. Silver" <mathelp@xxxxxxxxxxxxxxxx> wrote in message
news:w6_Se.12328$qY1.6372@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Liviu wrote:
>
>> Then please define what the "x" in "sin(x) / x" is supposed to mean.
>
> It's a real variable.

Yes, that too. But it also appeared to indicate the arclength in your
previous diagram, therefore my question.

If you want to move this to calculus / power series then that's fine with me
and I won't argue further. But, just as a matter of personal taste, I find
it better suited, and probably more appropriate for the bright-high-school
level the OP was alluding to, to keep this in the realm of geometry - while
identifying the minimum set of reasonable assumptions (e.g. a bounded set of
reals has a sup) required for the expected result. One can always go to
calculus later, reconcile the analysis with the geometry and formally prove
those assumptions at another level.



.

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