应用洛必达法则:
lim(x-tanx)/x^2
=lim(x-tanx)/limx^2
=lim(x-tanx)'/lim(x^2)'
=lim(1-(secx)^2)/lim(2x)(再次应用洛必达法则)
=lim(1-(secx)^2)'/lim(2x)'
=lim(-2tanx(secx)^2)/2
=-limsinx/(cosx)^3
=0/1=0,1,解法一:(泰勒公式法)
原式=lim(x->0)[(x-x-x³/3+o(x³))/x²] (应用泰勒公式展开)
=lim(x->0)[(-x³/3+o(x³))/x²]
=lim(x->0)[-x/3+o(x)...,3,