Çó½âlim(1 - x)tan90¡ãx x¡ú1

lim(1-x)tanx¦Ð/2 =lim(1-x)/(cosx¦Ð/2)=lim -1/(-¦Ð/2sinx¦Ð/2)=2/¦Ð x¡ú1


XÇ÷ÓÚ0,Çó¼«ÏÞlim[(1 - cosX)/(XtanX)]

xÇ÷ÏòÓÚ0ʱ£¬1-cosxÇ÷ÏòÓÚ£¨1/2£©£¨sinx)^2,Ç÷ÏòÓÚ(1/2)x^2,tanxÇ÷ÏòÓÚx,ËùÒÔ¼«ÏÞµÈÓÚ1/2 lim(X->0)[(1-cosX)/(XtanX)]=lim(X->0)[sin(x/2)]^2...


1/xµÄtanx´Î·½,Ç÷ÓÚ0+µÄ¼«ÏÞΪʲô²»ÊÇe?

1¡¢lim¦Õ(x)¡ú0(1+¦Õ(x))1¦Õ(x)=e 2¡¢lim¦Õ(x)¡ú¡Þ(1+1¦Õ(x))¦Õ(x)=e Æäʵ¹Ø¼ü¶¼ÊÇ1¡Þ²ÅÍùÕâ¸ö½Ç¶ÈÀ´¿¼ÂÇ¡£ºÜÃ÷ÏÔÕâÀïÊÇ...


ÔÚxÇ÷ÏòÓÚ0ʱ,Çó(1/x)tanxµÄ¼«ÏÞ.ÎÊ(1/x)tanx±ä³Ée...

ÕâÊÇÀûÓÃÁ˸´ºÏº¯ÊýÇó¼«Ï޵ķ¨Ôò!¼´lim(x¡úx0)f[g(x)]=lim(u¡úu0)f(u)=AËùÒÔlime^tanxln(1/x)=lime^lim(tanxln(1/x))ÔÙÓÃÂ屨´ï·¨Ôò¾Í¿ÉÒÔÇó³öÆä¼«ÏÞÁË...


1¡¢Çó¼«ÏÞlim(1/x - cotx) ,xÇ÷½üÓÚ02¡¢µ±0

(1)lim(x->0) (1/x -cotx)=lim(x->0) (1/x -1/tanx)=lim(x->0) (tanx-x)/(xtanx) (0/0)=lim(x->0) ( (secx)^2 -1 )/ ( x(secx)^2 ...


limx¡ú0 tanx - 1ΪÈý½×Ôõô¿´³öÀ´µÄ,Ì©ÀÕ¹«Ê½²»»áÓÃ,Óñð...

tanx-x)/xÁ¢·½ =limx¡ú0 (secƽ·½x-1)/3xƽ·½ =limx¡ú0 (tanƽ·½x)/3xƽ·½ =limx¡ú0 (xƽ·½)/3xƽ·½ =1/3 ËùÒÔ x¡ú0ʱ£¬ tanx-xÊÇxµÄ3½×ÎÞÇîС¡£


Çó¸ßÊÖ½â´ð¸ßÊý¼«ÏÞÎÊÌâ,I=lim(tanx)^ln(1 - x)µÄ¼«ÏÞ...

tanx ~ x ln (1-x) ~ -x Ô­À´¼«ÏÞ=x^(-x) = e^(-x lnx )xlnx = lnx /(1/x) => 1/x /£¨-1/x^2) = -x ËùÒÔÔ­À´¼«ÏÞ=1 ...


xÇ÷ÏòÓÚ0,x - ln(1+tanx)¿ÉÒÔÖ±½ÓдµÈ¼ÛÓÚx - ln(1+x)Âð...

1+tanx)xln(1+x)=limx¡ú0xln(1+tanx)x2limx¡ú0xln(1+x)x2=limx¡ú0xtanx12tan2...


Çó¼«ÏÞ:ÓõȼÛÎÞÇîСÁ¿.lim(xÇ÷½üÓÚ0¸º)(1 - ¸ùºÅÏÂcosx...

lim(x¡ú0) (1-¡Ìcosx)tanx / (1-cosx)^(3/2)=lim (1-¡Ìcosx)(1+¡Ìcosx)tanx / (1-cosx)^(3/2)(1+¡Ìcosx)=lim (1-cosx)tanx / (1-cosx)^(3/2.


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