1. lim (1 + 1/x)^x = e
x→∞
2. lim (1 + a/x)^x = e^a
x→∞
3. lim (e^x - 1)/x = 1
x→0
4. lim (a^x - 1)/x = ln a, where a > 0
x→0
5. lim [ln(1 + x)]/x = 1
x→0
6. lim ln x / (x - 1) = 1
x→0
更新1:
6. lim ln x / (x - 1) = 1 x→1
Proof of Limit Formulae
2008-08-18 4:58 am
Please prove the following expression completely
1. lim (1 + 1/x)^x = e
x→∞
2. lim (1 + a/x)^x = e^a
x→∞
3. lim (e^x - 1)/x = 1
x→0
4. lim (a^x - 1)/x = ln a, where a > 0
x→0
5. lim [ln(1 + x)]/x = 1
x→0
6. lim ln x / (x - 1) = 1
x→0
1. lim (1 + 1/x)^x = e
x→∞
2. lim (1 + a/x)^x = e^a
x→∞
3. lim (e^x - 1)/x = 1
x→0
4. lim (a^x - 1)/x = ln a, where a > 0
x→0
5. lim [ln(1 + x)]/x = 1
x→0
6. lim ln x / (x - 1) = 1
x→0
回答 (1)
2008-08-18 7:16 am
✔ 最佳答案
As follows:圖片參考：http://hk.geocities.com/stevieg_1023/0po1.gif
圖片參考：http://hk.geocities.com/stevieg_1023/0po2.gif
圖片參考：http://hk.geocities.com/stevieg_1023/0po3.gif
收錄日期: 2021-04-22 00:37:00
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