Re: limit was Re: Limes

From: William Elliot (marsh_at_privacy.net)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 06:02:45 -0800

On Mon, 21 Feb 2005, Robin Chapman wrote:
> Peter wrote:
>
>> I need help to prove
>>
>> lim x^(1 - cos(x))
>> x -> 0
>
> Take logarithms: you get
> (1 - cos x)log x.
>
= (1 - cos x)/(log x)^-1

By l'Hospital
(sin x)/(-(1/x)(log x)^-2)
= -(sin x)(log x)^2 /x