对tanx在x=0处进行Taylor展开得：tanx=x (x^3/3) o(x^4)对sinx在x=0处进行Taylor展开得：sinx=x-(x^3/6) o(x^4)∴tanx-sinx=[(1/3)-(-1/6)]x^3 o(x^4)=x^3/2 o(x^4)即：lim(x→0)[(tanx-sinx)/(x^3)]=1/2lim(x→0)[(tanx-sinx)/(x^4)]=0故tanx-sinx是x的3阶无穷小量，
