Question

洛必达法则？

这个等号怎么化的

Answer 1

=lim(x趋于π/2）(sinx/sin3x)·
Lim(x趋于π/2）（cos3x/cosx）
=sin（π/2）/sin（3π/2）·lim(cos3x/cosx)
=-lim(x趋于π/2）（cos3x）'/(cosx)'
=-lim(x趋于π/2）（-3sin3x）/(-sinx)
=-lim(x趋于π/2）(3sin3x/sinx)
=-3

Answer 2

lim(x->π/2) tanx/tan(3x)
=lim(x->π/2) cot(π/2-x)/cot(3π/2-3x)
=lim(x->π/2) tan(3π/2-3x)/tan(π/2-x)
=lim(x->π/2) (3π/2-3x)/(π/2-x)
=3lim(x->π/2) (π/2-x)/(π/2-x)
=3

Answer 3

直接把pi/2带入cos3x和cosx中去

追问

代入以后分子分母都是0啊怎么办

追答

说错了是带入sinx和sin3x中，然后对cos3x和cosx用洛必达

追问

Cos洛必达之后还是分子分母都是0