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2Â¥2015-11-28 09:23:59
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xiangxiang32

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3Â¥2015-11-28 09:26:11
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--power

½ð³æ (СÓÐÃûÆø)

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Edstrayer: ½ð±Ò+5, Latex·¢Ìû 2015-11-28 09:57:13
ÒýÓûØÌû:
3Â¥: Originally posted by xiangxiang32 at 2015-11-28 09:26:11
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4Â¥2015-11-28 09:49:09
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xiangxiang32

гæ (ÕýʽдÊÖ)

ÒýÓûØÌû:
4Â¥: Originally posted by --power at 2015-11-28 09:49:09
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\ln \lim_{x\to \infty} (\frac{1}{x}+2^{{1}{x}})^x
=\lim_{x\to \infty}\ln(\frac{1}{x}+2^{{1}{x}})^x
=\lim_{x\to \infty}x\ln(\frac{1}{x}+2^{{1}{x}})
=\lim_{x\to \infty}\frac{\l ...

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5Â¥2015-11-28 10:08:00
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--power

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
5Â¥: Originally posted by xiangxiang32 at 2015-11-28 10:08:00
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...

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6Â¥2015-11-28 11:32:03
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--power(Edstrayer´ú·¢): ½ð±Ò+2, лл²ÎÓëÓ¦Öú 2015-11-29 00:54:51
ԭʽ=limx¡ú¡Þ e^(x*ln(1/x+2^(1/x)))
Áît=1/x,Ôòlimx¡ú¡Þ ln(1/x+2^(1/x))/(1/x)
            =limt¡ú0 ln(t+2^t)/t
            =limt¡ú0  (1+(2^t)*in2)/(t+2^t)¡¤¡¤¡¤Â屨´ï·¨Ôò
            =1+ln2
Ôòԭʽ=e^(1+ln2)
7Â¥2015-11-29 00:29:20
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--power

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
7Â¥: Originally posted by ²ËÄñÁõÓî at 2015-11-29 00:29:20
ԭʽ=limx¡ú¡Þ e^(x*ln(1/x+2^(1/x)))
Áît=1/x,Ôòlimx¡ú¡Þ ln(1/x+2^(1/x))/(1/x)
            =limt¡ú0 ln(t+2^t)/t
            =limt¡ú0  (1+(2^t)*in2)/(t+2^t)¡¤¡¤¡¤Â屨´ï·¨Ôò
            =1+ln2
Ôòԭʽ ...

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8Â¥2015-11-29 08:37:24
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--power(Edstrayer´ú·¢): ½ð±Ò+2 2015-12-18 02:07:12
Lim{[2^(1/x)+1/x]^x,x-->0}
=Lim{{2^(1/x)*{1+1/[2^(1/x)*x]}}^x , x-->0}
=2*Lim{{1+1/[2^(1/x)*x]}^x , x-->0}
Áîu=2^(1/x)
x=Ln2/Lnu
ԭʽ=2*Lim{[1+Lnu/(u*Ln2)]^(Ln2/Lnu) , u-->1}
=2*Lim{{[1+Lnu/(u*Ln2)]^(u*Ln2/Lnu)}^(1/u) , u-->1}
=2*Lim{{[1+Lnu/(u*Ln2)]^(u*Ln2/Lnu)} , u-->1}
ÔÙÁît=Lnu/(u*Ln2)
ԭʽ=2*Lim{{[1+t]^(1/t)} , t-->¡Þ}
=2*e
9Â¥2015-12-01 09:13:09
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