Re: [微積] 羅比達求極限
※ 引述《pop10353 (卡卡:目)》之銘言：
: a^x + b^x (1/x)
: lim ( ___________________) a,b>0
: 2
: x-> 0+
: 唯一的提示是用羅必達..
＝lim Exp[(1/x)*ln[a^x+b^x]] ＝ Exp[lim (1/x)*ln[(a^x+b^x)/2]]
ln[(a^x+b^x)/2]
＝Exp[lim ────────]
x->0+ x
By L'hopital
(a^x*ln[a]+b^x*ln[b])/(a^x+b^x)
＝ Exp[────────────────] | x=0+
1
＝Exp[(ln[a]+ln[b])/2] ＝√(ab)
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◆ From: 114.24.62.187
推
03/26 21:20, , 1F
03/26 21:20, 1F
→
03/26 21:21, , 2F
03/26 21:21, 2F
terribly sorry, I include the factor 1/2 in the function ln [f(n)]
on my paper, so the factor can be cancel out on the 3rd line, hence
I neglected the factor 1/2 in the first two lines.
※ 編輯: Strogatz 來自: 114.24.62.187 (03/26 21:29)
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