x→π/2
lim (sinx-1)*(tanx)
还原,t=π/2-x
=lim(t→0) (sin(π/2-t)-1)*(tan(π/2-t))
=lim (cost-1)*(cott)
=-lim (1-cost)cost / sint
利用等价无穷小:1-cosx~x^2/2,sinx~x
=-lim t^2 / 2t * lim cost
=0
有不懂欢迎追问`~
x→π/2
lim (sinx-1)*(tanx)
还原,t=π/2-x
=lim(t→0) (sin(π/2-t)-1)*(tan(π/2-t))
=lim (cost-1)*(cott)
=-lim (1-cost)cost / sint
利用等价无穷小:1-cosx~x^2/2,sinx~x
=-lim t^2 / 2t * lim cost
=0
有不懂欢迎追问`~