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

Lee Rudolph wrote:
> N. Silver writes:
>>Lee Rudolph wrote:

>>> From this it follows that, *if you believe* that sin
>>> has a (non-zero) derivative *at all*, at any point,
>>> then its derivative is cos. Can that belief be
>>> justified without assuming the limit under consideration?
>>> I suspect it can, by further geometric argument using the
>>> helix parametrized by x \mapsto (cos(x), sin(x), x).

>>If you have such an argument, maybe we can go
>>back to the definition of derivative and prove the
>>limit is 1. Please give your geometric argument.

> My use of the verb "suspect" was intended to indicate that
> I was making this up as I went along. I don't have any such
> argument at the moment. If I think of one, despite all my
> efforts to do something else today, I'll post it.

fair enough


.

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