Re: can you find the limit of this function?
From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 07/16/04
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Date: Fri, 16 Jul 2004 02:19:43 -0600
In article <baa549eb.0407152255.2b987562@posting.google.com>,
max1974isome@hotmail.com (Max) wrote:
> Brute force calculating gives the limit of
>
> h
> 3 - 1
> -------
> h
>
> as approximately 1.09 when h approaches 0.
>
> How can I find that algebraically without
> calculus?
>
> Using the squeezing theorem I was able to
> confirm its range between 1 and 1.2817
> (= 4-e). But that's as close as I can get.
>
> any ideas for an exact answer?
>
> thanks,
> Max Schmeder
>
> (to reply by email, remove the year from my address)
Since 3^0 = 1, you have (3^h - 3^0)/h, whose limit will be the
derivative of 3^x with respect to x, evaluated at x = 0, which is ln(3).
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