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

"N. Silver" <mathelp@xxxxxxxxxxxxxxxx> 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.

Lee Rudolph
.

Relevant Pages

  • Re: sin x / x tends to 1...
    ... N. Silver wrote: ... > Lee Rudolph wrote: ... >> then its derivative is cos. ... Prev by Date: ...
    (sci.math)
  • Re: sin x / x tends to 1...
    ... Lee Rudolph wrote: ... > From this it follows that, *if you believe* that sin ... > then its derivative is cos. ... Prev by Date: ...
    (sci.math)
  • Re: sin x / x tends to 1...
    ... Lee Rudolph wrote: ... > From this it follows that, *if you believe* that sin ... > then its derivative is cos. ... Prev by Date: ...
    (sci.math)
  • Re: sin x / x tends to 1...
    ... > N. Silver writes: ... >>Lee Rudolph wrote: ... >>> then its derivative is cos. ... >>> I suspect it can, by further geometric argument using the ...
    (sci.math)
  • Re: Automorphisms of the Klein curve
    ... and I suspect there are 3. ... I just gave up and went off to eat dinner). ... Lee Rudolph ...
    (sci.math)
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