数学达人帮助求极限!当x->0时sin(x)=x+o(x)x*cos(x)=x-x^3/2!+o(x^3)sin(x)^3=x^3+o(x)lim(sin(x)-x*cos(x)/sin(x)^3=1/2请问错在哪里?谢谢!

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/20 15:20:33
数学达人帮助求极限!当x->0时sin(x)=x+o(x)x*cos(x)=x-x^3/2!+o(x^3)sin(x)^3=x^3+o(x)lim(sin(x)-x*cos(x)/sin(x)^3=1/2请问错在哪里?谢谢!

数学达人帮助求极限!当x->0时sin(x)=x+o(x)x*cos(x)=x-x^3/2!+o(x^3)sin(x)^3=x^3+o(x)lim(sin(x)-x*cos(x)/sin(x)^3=1/2请问错在哪里?谢谢!
数学达人帮助求极限!
当x->0时
sin(x)=x+o(x)
x*cos(x)=x-x^3/2!+o(x^3)
sin(x)^3=x^3+o(x)
lim(sin(x)-x*cos(x)/sin(x)^3=1/2
请问错在哪里?
谢谢!

数学达人帮助求极限!当x->0时sin(x)=x+o(x)x*cos(x)=x-x^3/2!+o(x^3)sin(x)^3=x^3+o(x)lim(sin(x)-x*cos(x)/sin(x)^3=1/2请问错在哪里?谢谢!
sinx=x-x^3/6+o(x^3)
(sinx-xcosx)/sinx^3=(-x^3/6+x^3/2)/x^3=1/3