Re: can you find the limit of this function?

From: Ronald Bruck (bruck_at_math.usc.edu)
Date: 07/16/04 

Date: Fri, 16 Jul 2004 09:04:05 -0700

In article <baa549eb.0407152255.2b987562@posting.google.com>, Max
<max1974isome@hotmail.com> 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?

WITHOUT calculus? Most unlikely. The limit is, by definition, the
derivative of f(x) = 3^x at x = 0.

--Ron Bruck

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