lim x->∞x²[1 - cos(1/x)]
= lim x->∞[1 - cos(1/x)] / (1/x²) (分子, 分母同时趋向於0,可利用洛必达法则)
= lim x->∞{0 - [-sin(1/x)] * [-x^(-2)]} / [-2x^(-3)]
= lim x->∞[sin(1/x)] / (2/x)(分子, 分母同时趋向於0,可利用洛必达法则)
= lim x->∞[cos(1/x) * (1/x)'] / (2/x)'
= lim x->∞[cos(1/x)] / 2
= cos(0) / 2
= 1/2