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

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.


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