《評論》Proof of limit

2008-11-10 5:47 pm
相關問題: https://hk.answers.yahoo.com/question/index?qid=20081020000051KK00400
更新1:

In fact we can use the Squeezing principle (Sandwich theorem) to prove it as follows: 圖片參考:http://i117.photobucket.com/albums/o61/billy_hywung/Nov08/Crazylim1.jpg aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

回答 (2)

2009-01-20 2:54 am
very good
2009-01-01 7:12 am
One point to be noted:

While expanding (1 + h)^x into binomial series, |h| should be less than 1 to ensure convergence!

Fortunately, 0 < x^(1/x) < e^(1/e) < 2 for x > 0.
Hence |h| = |x^(1/x) - 1| < 1.


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