更新1:
Prove for a constant k-- limit as x-->infinity (x*sin(k/x)) = k?
Prove for a constant k limit as x-->infinity (x*sin(k/x)) = k?
回答 (2)
2017-01-10 8:11 am
u = k/x
x = k/u
x * sin(k/x) =>
(k/u) * sin(u) =>
k * sin(u)/u
As x goes to infinity, k/x goes to 0
The limit of sin(u)/u as u goes to 0 is 1
k * 1 => k
x = k/u
x * sin(k/x) =>
(k/u) * sin(u) =>
k * sin(u)/u
As x goes to infinity, k/x goes to 0
The limit of sin(u)/u as u goes to 0 is 1
k * 1 => k
2017-01-10 8:10 am
just let [ k / x ] = w then take the limit as w ----> 0
收錄日期: 2021-04-24 00:05:56
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170110000916AA46f6Q