Re: Another question about derivatives

On 26 Dec 2005 18:05:14 -0800, "Dave L. Renfro" <renfr1dl@xxxxxxxxx>
wrote:

>The World Wide Wade wrote:
>
>>> I see we're having a little too much eggnog
>>> during the holidays. [f(x)-f(0)]/(x-0) = f'(c_x),
>>> right? So if f'(c_x) -> 0, then ...
>
>quasi wrote:
>
>> then lim f'(x) --> 0 as x --> 0.
>>
>> What am I missing?
>
>Well, actually you don't know that f'(x) --> 0 as x --> 0
>simply from f'(c_x) --> 0 (the stronger limit, where x --> 0,
>might not exist, while the weaker limit, where x approaches
>zero in such a way that x is always equal to one of the c_x's,
>might exist), although of course we do know that f'(x) --> 0
>because this was in the original poster's hypothesis. [I'm not
>suggesting that you didn't recognize this as in the original
>hypothesis, by the way. Indeed, I assume this was part of
>your confusion, namely that the argument seems to only prove
>something we already knew. My point is that the argument
>doesn't even do this as far as I can tell.]
>
>I believe what's going on is that in the equation
>
> [f(x)-f(0)] / (x-0) = f'(c_x),
>
>if we take the limit as x --> 0 of both sides, then the
>left side becomes the definition of f'(0) and the right
>side becomes 0.
>
>Dave L. Renfro

Thanks, Dave.

I did finally realize what I was missing.

quasi
.

Relevant Pages

  • Re: Another question about derivatives
    ... >> I see we're having a little too much eggnog ... quasi wrote: ... > What am I missing? ... might not exist, while the weaker limit, where x approaches ...
    (sci.math)
  • Re: Another question about derivatives
    ... quasi wrote: ... > I did finally realize what I was missing. ... I began writing my post. ... Dave L. Renfro ...
    (sci.math)
  • Re: How can I get mouse shortcuts to work in Excel
    ... Sounds like also missing the right-click on sheet tab menu. ... Gord Dibben Excel MVP ... > There is no right click menu (context menu missing). ... >> Hi Dave, Thanks for the response. ...
    (microsoft.public.excel.setup)
  • Re: RAMPS Party congrats!!!
    ... transports. ... Only when the alcohol is NOT missing. ... Also special thanks to Dave ...
    (rec.arts.movies.production.sound)
  • Re: Gestational diabetes: answers to my earlier questions
    ... Dave and Ozgirl, your concern truly is very kind, even if you have been ... missing some of my posts in the avalanche... ... reputation for treating GD so I have no reason to believe I am being ...
    (alt.support.diabetes)