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dragonship: ½ð±Ò+18, ¡ï¡ï¡ïºÜÓаïÖú 2015-09-01 17:34:50
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5Â¥: Originally posted by peterflyer at 2015-09-01 15:33:52
ÒÑÖª Lim{{sqrt-1}/ , x-->0}=2,
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I=Lim{{1/sqrt*}/ , x-->0}
=Lim{1*/3, x-->0}=2
¹Ê£ºLim{f(x), x-->0}=6...

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6Â¥2015-09-01 15:35:40
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£¨1£© Lim{[(x^2-1)/(x^2+1)]^x£¬x-->¡Þ}
          ÁîI = Lim{[1-2/(x^2+1)]^x£¬x-->¡Þ}
Lim{LnI£¬x-->¡Þ}=Lim{x*Ln[1-2/(x^2+1)], x-->¡Þ}
              =Lim{Ln[1-2/(x^2+1)]/(1/x) , x-->¡Þ}
             =Lim{1/[1-2/(x^2+1)]*(-2)*2*x/(x^2+1)^2/(-1/x^2) , x-->¡Þ}
             =Lim{4*x^3/(x^2+1)^2 , x-->¡Þ}
              =0
¹Ê£º Lim{[(x^2-1)/(x^2+1)]^x£¬x-->¡Þ}=I=exp(LnI)=exp(0)=1
3Â¥2015-09-01 15:24:16
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Edstrayer

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4Â¥2015-09-01 15:32:35
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ÒÑÖª Lim{{sqrt[1+f(x)*Sinx]-1}/[exp(3*x)-1] , x-->0}=2,
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I=Lim{{1/sqrt[1+f(x)*Sinx]*[Cosx*f(x)+x*f'(x)]}/[3*exp(3*x)] , x-->0}
=Lim{1*[f(x)+0]/3, x-->0}=2
¹Ê£ºLim{f(x), x-->0}=6
5Â¥2015-09-01 15:33:52
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