number e

👨🏻‍🏫 學術台數學

Larry

2010-10-03 3:20 am

find lim(x→0) In(1+2x)/x
唔該步驟詳細小小...

更新1:

個ans係岩但係我唔明你做咩==

更新2:

可唔可以唔用L'hospital's rule /微分做==我未學

回答 (1)

六呎將軍

2010-10-04 6:20 am

✔ 最佳答案

lim(x→0) In(1+2x)/x

= lim(x→0) In [(1+2x)1/x]

= ln {lim(x→0) [(1+2x)1/x]}

For lim(x→0) [(1+2x)1/x]:

lim(x→0) [(1+2x)1/x] = lim(x→0) {[(1+2x)1/(2x)]2}

= {lim(x→0) [(1+2x)1/(2x)]}2

= e2

Hence:

lim(x→0) In(1+2x)/x = ln e2 = 2

參考: Myself

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