求 极限~微积分
问题描述:
求 极限~微积分
lim tanx/tan(3x) 当 x 趋进pie/2
答
lim(x→π/2) tanx/tan(3x)
=lim(x→π/2) [sinx/sin(3x)×cos(3x)/cosx]
=-lim(x→π/2) cos(3x)/cosx洛必达法则
=-lim(x→π/2) 3sin(3x)/sinx
=3