1/X^2-1/(x*tanx)=(tanx-x)/(x^2*tanx)
tanx是x的等价无穷小(x趋向于0)
原式可化为
lim(x趋向于0)(tanx-x)/(x^3) 分式,分子同时求导
=lim(x趋向于0)[(secx)^2-1]/(3*x^2) (secx)^2-1=(tanx)^2
=lim(x趋向于0)[(tanx)^2]/(3*x^2) tanx是x的等价无穷小(x趋向于0)
=lim(x趋向于0)[x^2]/(3*x^2)
=1/3
用罗必塔法则啊,分子分母求导