推 totowo:L'Hospital's Rule 要求分子分母的極限 218.79.185.126 12/02
→ totowo:分子分母的極限都為0 218.79.185.126 12/02
※ 編輯: littlefive 來自: 129.97.204.91 (02/28 11:04)
※ 引述《binbin1 ( )》之銘言：
: （3）0的0次方為什麼無意義
(SORRY because I can't type Chinese now!)
First, a^0=1 because mathmatician simply define
a^0 = lim a^x = 0
x->0
Second, usually we say 0^0=1
you can try many software for example Matlab, Maple
consider 0^a=0 and a^0=1 for any a>0
we have a problem:
lim x^a = 0 lim a^x = 1
x->0 x->0
I believe the true reason is the below
lim x^x = 1
x->0+
Proof.
Say the value of the above is k. Now ln is continuous so
lim xln(x) = ln(k)
x->0+
But
ln(x)
lim xln(x) = lim ------- = lim (-x) = 0 by L'Hospital's Rule
x->0+ x->0+ 1/x x->0+
so
ln(k) = 0
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◆ From: 129.97.204.91
※ 編輯: littlefive 來自: 129.97.204.91 (12/02 11:52)
※ 編輯: littlefive 來自: 129.97.204.91 (12/02 12:06)