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lim極限數1題........
回答 (2)
2007-09-12 4:59 am
✔ 最佳答案
如下:圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Sep07/Crazylim1.jpg
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Sep07/Crazylim2.jpg
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Sep07/Crazylim3.jpg
2007-09-11 21:41:08 補充：
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參考: My maths knowledge
2007-09-12 4:52 am
lim (x→∞) [(x-2)/(x+1)]^x
= lim (x→∞) [(1-2/x)/(1+1/x)]^x
Since 1-2/x < 1+1/x for all x > 0
Therefore, [(1-2/x)/(1+1/x)] < 1
For all y < 1
y^x approaches 0 for x tends to infinity
Therefore,
lim (x→∞) [(1-2/x)/(1+1/x)]^x
= 0
= lim (x→∞) [(1-2/x)/(1+1/x)]^x
Since 1-2/x < 1+1/x for all x > 0
Therefore, [(1-2/x)/(1+1/x)] < 1
For all y < 1
y^x approaches 0 for x tends to infinity
Therefore,
lim (x→∞) [(1-2/x)/(1+1/x)]^x
= 0
收錄日期: 2021-04-30 22:29:30
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070911000051KK03698