lim<x to infinity>(1+(3/x))^x (ans: e^3)
why the ans invole e?
why not calculated as follow?
(lim1 + 3lim(1/x))^x
=(1+3(0))^x
=1??
thx
更新1:
讀文學的學生: but why the following method is not correct? (lim1 + 3lim(1/x))^x =(1+3(0))^x =1??
lim(1+(3/x))^x
2012-08-20 12:42 am
i want to ask how to solve the problem....
lim<x to infinity>(1+(3/x))^x (ans: e^3)
why the ans invole e?
why not calculated as follow?
(lim1 + 3lim(1/x))^x
=(1+3(0))^x
=1??
thx
lim<x to infinity>(1+(3/x))^x (ans: e^3)
why the ans invole e?
why not calculated as follow?
(lim1 + 3lim(1/x))^x
=(1+3(0))^x
=1??
thx
回答 (2)
2012-08-20 2:49 am
✔ 最佳答案
lim(x→∞)[1+(3/x)]^x=lim(x→∞){[1+1/(x/3)]^(x/3)}^3
=e^3
Remember,
lim(x→∞)[(1+1/n)^n]=e
參考: me
2012-08-20 1:26 am
記唔記得呢條式:
lim(n-->infinity)(1+x/n)^n = e^x = 1+x+(x^2)/2! + (x^3)/3! + ........
咁對番D位,個答案就係e^3啦
2012-08-19 20:22:20 補充：
x係變數,你唔可以唔理個x次方而張limit擺入(1+3/x)
你咁樣做只係求左個y既limit,之後先再張舊數放番入X次方,咁樣既話就唔係求成舊數既limit
2012-08-19 20:29:23 補充：
個y係指番個(1+3/x)
lim(n-->infinity)(1+x/n)^n = e^x = 1+x+(x^2)/2! + (x^3)/3! + ........
咁對番D位,個答案就係e^3啦
2012-08-19 20:22:20 補充：
x係變數,你唔可以唔理個x次方而張limit擺入(1+3/x)
你咁樣做只係求左個y既limit,之後先再張舊數放番入X次方,咁樣既話就唔係求成舊數既limit
2012-08-19 20:29:23 補充：
個y係指番個(1+3/x)
參考: me, me, me
收錄日期: 2021-04-20 13:12:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120819000051KK00407