Evaluate the following limits
x^2
lim ╭ x^2 +1 ╮
--------------
x－＞無限 ╰ x^2 -1 ╯
依題點做..括號打得唔好..意思係成個既x二次方
limits
2006-10-17 6:50 am
回答 (1)
2006-10-17 7:03 am
✔ 最佳答案
Let y = x^2. Then the required limit equalslim[y -> +∞] [(y + 1) / (y - 1)]^y
= lim[y -> +∞] [(1 + (1 / y)) / (1 - (1 / y))]^y
= lim[y -> +∞] (1 + (1 / y))^y / lim[y -> +∞](1 - (1 / y))^y
Note that lim[y -> +∞] (1 + (1 / y))^y = e and
lim[y -> +∞] (1 - (1 / y))^y
= lim[y -> +∞] [(1 + (-1 / y))]^y
= e^(-1)
Thus the limit is e / e^(-1) = e^2
收錄日期: 2021-04-12 22:34:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061016000051KK05012