求极限中无穷小代换和高阶无穷小略去问题

求极限中无穷小代换和高阶无穷小略去问题
Lim (1/x^2-cot^2x)=lim (1/x^2-1/tan^2x)=lim(tan^2x-x^2)/x^2*tan^2x=lim(tan^2x-x^2)/x^4
=lim(tan^2x/x^4)=lim2tanxsec^2x/4x^3=lim2xsec^2x/4x^3=limsec^2/2x^2=lim2sec^2xtanx/4x=limsec^2x*x/2x=limsec^2x/2=1/2 (x趋向于0)
题目中由于x^2是高阶无穷小略去