lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,

lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) =lim(x趋向于0)[(sinx/cosx-sinx)]/x(sinx)^2
=lim(x趋向于0)[1-cosx)/x(sinx)=lim(x趋向于0)2(sinx/2)^2/x2sinx/2cosx/2
=1/2lim(x趋向于0)[sinx/2/x/2)(1/cosx/2=lim(x趋向于0)1/cosx/2=1/2
两个重要极限 lim(x趋向于0)sinx/x=1