lim (tanx-sinx)/x^2*sinx x趋于0求极限怎么解

lim (tanx-sinx)/x^2*sinx x趋于0求极限怎么解
lim (tanx-sinx)/x^2*sinx x趋于0求极限怎么解

lim (tanx-sinx)/x^2*sinx x趋于0求极限怎么解
lim (tanx-sinx)/(x^2*sinx)
= limtanx (1-cosx)/(x^2*sinx) (等价无穷小代换)
= limx (x^2/2)/(x^2*x) = 1/2

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