lim(x→0)(x^x^x) = ?
回答 (1)
2006-12-13 4:28 am
✔ 最佳答案
lim(x->0+) x^x=lim(x->0+) e^(xlnx)
=lim(x->0+) e^lnx/(1/x)
=lim(x->0+) e^(1/x)/(-1/x^2) (L'Hospital Rule)
=lim(x->0+) e^-x
=e^0
=1
lim(x->0+) x^(x^x)=0 since x->0 and x^x->1
2006-12-12 20:37:37 補充：
如果是lim(x→0) x^(x^x)就一定undefined因為這個function的domain無可能負數因而左極限不存在
收錄日期: 2021-04-12 21:21:49
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061212000051KK03603