若x为1阶无穷小,则2sin(x/2)(1+secx/2)sinx/4sinx/4的阶数为?
问题描述:
若x为1阶无穷小,则2sin(x/2)(1+secx/2)sinx/4sinx/4的阶数为?
答
2sin(x/2)(1+secx/2)sinx/4sinx/4
=4sin(x/4)cos(x/4)[(1+cos(x/2))/cos(x/2)]sinx/4sinx/4
=4sin(x/4)cos(x/4)[(cos(x/4))^2/cos(x/2)]sinx/4sinx/4
=4sin(x/4)^3 cos(x/4)^3 /cos(x/2)
=sin(x/2)^3 /2cos(x/2)
为X的三阶无穷小
(好难打啊,将就看吧…… ^2为二次方的意思,三次方同理)