Re: [極限]
※ 引述《Qmmm (Q蛆蛆)》之銘言：
: 標題: [極限]
: 時間: Wed Aug 27 15:53:07 2008
: 1. π x
: lim ( x - π ) = ?
: x->∞
:
:
:
x
π 做Taylor展開
2
(㏑π) 2
1 + ㏑πx + ----- x + ......
2!
n
∞ (㏑π) n
= Σ ----- x
n=0 n!
π x 4 x
lim ( x - π ) < lim ( x - π )
x->∞ x->∞
n
4 ∞ (㏑π) n
= lim [ x - Σ ----- x ] = -∞
x->∞ n=0 n!
: 2. 1 1 1
: lim --------- ( --------- - --- ) = ?
: x->0+ x^(1/3) sin x x
:
x - sinx
= lim ----------------
x->0+ 4/3
x sinx
3 5
x x
x - (x - --- + --- - .... )
3 5
= lim ------------------------------------------
x->0+ 4/3 x^3 x^5
x ( x - --- + --- - .... )
3 5
= 0
: 3.
: lim [x^(1/3)]*e^(cosπ/x) = ?
: x->0
:
cosπ= -1
let y = 1/x , when x>0
Y = -y = |1/x| , when x < 0
=>
-1/3 -y 1
lim y e = lim ------------- = 0
y->∞ y->∞ y^(1/3) e^y
-1/3 Y
lim Y e = ∞
Y->∞
所以左右極限不相等
--
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◆ From: 140.112.243.42
※ 編輯: yuyumagic424 來自: 140.112.243.42 (09/05 14:46)
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