Re: limit was Re: Limes

From: The World Wide Wade (waderameyxiii_at_comcast.remove13.net)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 11:56:31 -0800

In article <cvcot4$1oa$1@south.jnrs.ja.net>,
 Robin Chapman <rjc@ivorynospamtower.freeserve.co.uk> wrote:

> > I need help to prove
> >
> > lim x^(1 - cos(x))
> > x -> 0
> >
> > I tried with x^(1 - cos(x)) = x / x^cos(x) and then l'Hospital rule but

Write x^(1 - cos(x)) = (x^x)^[(1-cos(x))/x]. Recall x^x -> 1 and
(1-cos(x))/x -> 0. Looks like 1^0 = 1 is the limit.