tanx/tan3x x→π/2
问题描述：
tanx/tan3x x→π/2
(1/x)^tanx x→0+ lin都省略了
答
考察罗比达法则
1,先整理
lim x->π/2 tanx/tan3x =(lim x->π/2 sinx/sin3x }*{lim x->π/2 cos3x/cosx }
=(-1)*{ lim x->π/2-3sin3x/(-sinx) } =3
2、先取对数,再用罗比达法则
lim x->0（1/x)^tanx =e^[lim x->0 (-tanxlnx) ]=e^[lim x->0 (-lnx) /cotx] =e^[lim x->0 (-1/x)/(-csc²x)]=e^[lim x->0 (sin²x)x]=e^[lim x->0 sinx *(sinx)x]=e^0=1