數學M2:first principle
回答 (2)
2010-12-04 1:40 am
✔ 最佳答案
dy/dx=lim(h->0) [ln(x+h)-lnx]/h
=lim(h->0) [ln(1+h/x)]/h
=lim(t->0) [ln(1+t)]/(tx) where t=h/x
=lim(t->0) [ln(1+t)^(1/t)]/x
=1/x (ln e) as (lim t->0 (1+t)^(1/t)=e)
=1/x
2010-12-04 1:38 am
You have to make use of the relation : e^x = lim (1 + hx)^(1/h) h tends to zero. Is this in the M2 syllabus?
收錄日期: 2021-04-26 14:02:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101203000051KK00825