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¥Ñ chongxe ©ó ¬P´Á¤T ¤­¤ë 11, 2005 2:37 pm


¬°¤°»òlim(1+1/x)^x¡@ ,¡@ x->infinite¡@¡@=¡@e

¬°¤°»ò e^xªº·L¤ÀÁÙ¬Oe^x

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¥Ñ Eclipse ©ó ¬P´Á¤­ ¤­¤ë 20, 2005 12:06 pm


¥ªÁä: ÂIÀ»ÁY©ñ; ¥kÁä: Æ[¬Ý­ì¹Ï

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µù¥U®É¶¡: 2005-01-29
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Re: [¼Æ¾Ç]°Ýe°ÝÃD

¥Ñ ¤¸­º ©ó ¬P´Á¤­ ¥|¤ë 21, 2006 6:36 pm


chongxe ¼g¨ì:¬°¤°»òlim(1+1/x)^x¡@ ,¡@ x->infinite¡@¡@=¡@e

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¥Ñ p ©ó ¬P´Á¥| ¥|¤ë 27, 2006 11:36 pm


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1.lim(1+1/n)^n ,n¡÷¡Û ,nÄÝ©óN
2.lim(1+1/1!+1/2!+1/3!+----+1/n!)  ,n¡÷¡Û, nÄÝ©óN

¦Ólim(1+1/x)^x=e  ,x¡÷¡Û ,xÄÝ©óR, ¬O»Ý­nµý©úªº.
µý©ú¤è¦¡, ¥i¥On=[x]

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¥Ñ linch6123 ©ó ¬P´Á¤é ¤­¤ë 07, 2006 11:39 pm


¤¸­º¼g¨ì:
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­Ylnx©Me^x  ¬°¤Ï¨ç¼Æ   «h lnxªº·L¤À = 1/x
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linch6123
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¥Ñ Errfree ©ó ¬P´Á¤T ¤­¤ë 10, 2006 1:04 am


¹ï f(x) ·L¤Àªº©w¸q¦p¤U:
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¨º»ò¹ï loga(x) ªº·L¤À, ´N¥i¥H¼g¦¨¦p¤U: (¥H¤U¥Î h ²Å, ¨Ó¥N´À ¡µx ³o­Ó¼W¶q²Å).
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§â 1/h ¥ý´£¥X¨Ó
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¨â­Ó Log ¬Û´î, µ¥©ó Log ¤º¨â­È¬Û°£
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§â¥~­±ªº 1/h §ì¨ì Log ¤º·í¦¸¤è.
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¦A§ì x ¨ì Log ¤º·í¦¸¤è, ©Ò¥H¥~­±´N­n¸É¤@­Ó 1/x .
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¨º Log ¤º´N¬O e ªº©w¸q¤F!
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·í a = e ®É, Loge(e) = Ln(e) = 1

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¥Ñ linch6123 ©ó ¬P´Á¤­ ¤­¤ë 12, 2006 5:59 pm


Errfree¤j¤jªº¸ÑÃDÁ`¬O²M·¡©öÀ´,«Ü³ßÅw§A¹Ï¤å¨Ã­Zªº¸Ñªk

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¡]1¡^ ¼Æ¦C a_n =(1+1/n)^n
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e=lim(1+1/n)^n ©Î e=1+1+1/2!+1/3!+¡K.1/n!+....

¡]2¡^ §Q¥Î§¨À½¥i¥H±o¨ì
lim(1+1/n)^n=lim(1+1/x)^x ¦b¦¹x¤£¤@©w­n¬°¾ã¼Æ

¡]3¡^ ©w¸qa^x ©Mlogx (¥Ha¬°©³)¤¬¬°¤Ï¨ç¼Æ
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(e^x)'=e^x

¡]4¡^ ¥Ñ­ì©l©w¸qe=lim(1+1/n)^n «h¹ï©ó©Ò¦³¹ê¼Æx
e^x=lim(1+1/n)^(nx) ©Î e^x=(1+1+1/2!+1/3!+¡K.1/n!+....)^x
¦ý§Ú­Ì¦b·L¿n¤À¾Ç²ß¹Lµ{¤¤³£¨Ï¥Î¤F
e^x=lim(1+x/n)^n ©Îe^x=(1+x+x^2/2!+¡K+.x^n/n!+......)
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e^x=lim(1+1/n)^(nx)=lim(1+x/n)^n ¥B
e^x=lim(1+1+1/2!+1/3!+¡K.1/n!+..)^x=(1+x+x^2/2!+¡K.x^n/n!+....)

¡i1¡j ln lim(1+1/n)^(nx)
=lim ln(1+1/n)^(nx) ¦]¬°lnx¬°³sÄò¨ç¼Æ©Ò¥Hlim¥i´£¨ì¥~­±
=x lim ln (1+1/n)^n
=x ln lim(1+1/n)^n
=x lne
=x



¡i2¡j ln lim(1+x/n)^n
=lim ln(1+x/n)^n
=lim n ln(1+x/n)
¥Ot =1/n
=lim ln(1+tx)/t (ù¥²¹F)
=lim x/(1+tx)
=x

¥Ñ¡i1¡j¡i2¡j©Mlnx¬°¤@¹ï¤@¨ç¼Æ±oe^x=lim(1+1/n)^(nx)=lim(1+x/n)^n


¡i3¡je^x =lim(1+1/n)^(nx)
= lim(1+x/n)^n
=1+1+1/2!+1/3!+¡K.1/n!+....

linch6123
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µù¥U®É¶¡: 2005-11-08

¥Ñ rainy ©ó ¬P´Á¤­ ¤­¤ë 12, 2006 9:18 pm


¡]3¡^ ©w¸qa^x ©Mlogx (¥Ha¬°©³)¤¬¬°¤Ï¨ç¼Æ
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(lnx)'=1/x
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¥Ñ linch6123 ©ó ¬P´Á¤» ¤­¤ë 13, 2006 1:43 am


[quote="rainy"]¡]3¡^ ©w¸qa^x ©Mlogx (¥Ha¬°©³)¤¬¬°¤Ï¨ç¼Æ
¥i¥H±o¨ì
(lnx)'=1/x
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½Ðµy¥[»¡©ú


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