Quod Erat Demonstrandum

2009/04/22

一些有關不能使用 l’Hôpital’s rule 的例子

Filed under: HKALE,Pure Mathematics — johnmayhk @ 9:31 上午
Tags: ,

昨天和同事討論 l’Hôpital’s rule,我就是忘記了一個例子,以說明就算運用 l’Hôpital’s rule 找到 \lim \frac{f'}{g'} (有限值),它也未必等於 \lim \frac{f}{g},今早補貼一下:

http://www.hkedcity.net/ihouse_tools/forum/read.phtml?forum_id=27877&current_page=&i=1222468&t=1220987

Mathworld 也記下了兩個例子,參考參考

http://mathworld.wolfram.com/LHospitalsRule.html

Opened question: 應該如何教 l’Hôpital’s rule?

2 則迴響 »

  1. May I know what the problem is for these few examples? Mathworld said “L’Hospital’s rule must sometimes be applied with some care, since it holds only in the implicitly understood case that g^'(x) does not change sign infinitely often in a neighborhood of infty.", but I tried to follow the proof of L’Hospital’s rule once more and don’t see where this is needed at all.

    迴響 由 Soarer — 2009/04/25 @ 1:06 下午 | 回覆


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