泰勒公式cosx=1-x^2/2!+x^4/4!+o(x^4)(1+x)^1/2=1+x/2+o(x)(1-x)^1/2=1-x/2+o(x)带入极限lim(x→0)(x^2/2+cosx-1)/{x^3[(1+x)^½-(1-x)^½]}=lim(x→0)(x^4/4!)/(x^3*x)=1/4!=1/24