Find the limit. Use l' Hospital's Rule where appropriate. If there is a more
elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why
lim In√x / x^2
x->∞
Calculus
2015-03-05 6:57 pm
回答 (3)
2015-03-06 3:41 am
✔ 最佳答案
The answer is as follows :圖片參考：https://s.yimg.com/lo/api/res/1.2/3iZgsnlxN_vQz4ZpY82hJg--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/https://farm9.staticflickr.com/8605/16535587250_f040d585c9_o.png
https://farm9.staticflickr.com/8605/16535587250_f040d585c9_o.png
2015-03-08 22:23:15 補充：
另法：
lim(n→∞) [(ln √x) / x²]
= lim(n→∞) [(1/2)(ln x) / x²]
= lim(n→∞) [(1/2)(d/dx)(ln x) / (d/dx)x²]
= lim(n→∞) [(1/2x) / (2x)]
= lim(n→∞) (1 / 4x²)
= 0
2015-03-09 00:03:44 補充：
明 白 ， 謝 謝 你 ！
2015-03-12 9:32 pm
Thanks u guys =)
2015-03-08 12:31 pm
考慮 ln√x = (1/2) ln x 會更方便。
收錄日期: 2021-04-18 15:02:49
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