lim(x→0)(x-arcsinx)/sinx^3(分母等价无穷小)
=lim(x→0)(x-arcsinx)/x^3 (0/0,洛必达法则)
=lim(x→0)[1-1/√(1+x^2)]/(3x^2)(通分)
=lim(x→0)[√(1+x^2)-1]/[√(1+x^2)*(3x^2)](极限运算法则)
=lim(x→0)[√(1+x^2)-1]/(3x^2)*lim(x→0)1/√(1+x^2)
=lim(x→0)[√(1+x^2)-1]/(3x^2)(分子等价无穷小)
=lim(x→0)1/2x^2/(3x^2)
=1/6