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From: eurms@apionet.or.jp (M_SHIRAISHI)
Newsgroups: fj.sci.math
Subject: Re: =?ISO-8859-1?Q?Quiz=5F06iv2004=3F=3F=3F=3F?=
Date: 17 May 2004 08:36:43 -0700
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Xref: ccsf.homeunix.org fj.sci.math:1122

"Y.N." wrote in message news:<c8agc1$q4a$1@nr1.vectant.ne.jp>...
>
> M_SHIRAISHI ????????:
>
>> ???m(_ _)m
>> 
>>>eurms@apionet.or.jp (M_SHIRAISHI) wrote in message >>news:<800c7853.0405151646.44cfa850@posting.google.com>...
>>>
>>># ?x ?????????d^y?f''(x)dx^2 ?????????????????
>>>?????????????????
>> 
>> ?x ?????????dy??f'(x)??x ????????????????
>> d^y?f''(x)dx^2 ????????????????????????????
>
>??????????????
>?x?x_1?x ??????(?)?


?y?f(x) ????d^2?f''(x)dx^2 ????---- ?????????

????dy?f'(x)??x ???????????????????????
??????????


dy?f'(x)??x ???????????????

d(dy)?d{f'(x)??x}?{f'(x)??x}???x ?{f''(x)??x ? f'(x)?(?x)'}??x

???????????x ? x_1?x.  ??????? x_1 ? x ?????????
?x ??????? x_1?x.  

????(?x)'?(x_1?x)'??1.

# ??????Cauchy ????????????????????????????
??????

(?x)'?(x_1?x)'?lim{?x?0}?[{x_1?(x??x)}?{x_1?x}]??x ?
?lim{?x?0}?(??x)??x?? ?1

????

{f''(x)??x ? f'(x)?(?x)'}??x ? {f''(x)??x ?f'(x)}??x
?f''(x)?(?x)^2?f'(x)??x

???d(dy) ? f''(x)?(?x)^2?f'(x)??x

?x ? dx ?????????d(dy) ? f''(x)?(dx)^2?f'(x)?dx

?x?0 ????x ??? (?x)^2 ??????????????????
f''(x)?(?x)^2 ??????d(dy) ? ?f'(x)??x ????????
???????????????????????


???????dy?f'(x)??x ???????????????????
??????dy?f'(x)??x ????????????????????
N Bourbaki ????????????????*??*??????