求极限.准确.lim(x>2分之派) tan3x分之tanx

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 19:14:14
求极限.准确.lim(x>2分之派) tan3x分之tanx

求极限.准确.lim(x>2分之派) tan3x分之tanx
求极限.准确.lim(x>2分之派) tan3x分之tanx

求极限.准确.lim(x>2分之派) tan3x分之tanx
lim(x→π/2) tanx/tan3x
=lim(x→π/2) sec^2x/[3sec^2(3x)]
=lim(x→π/2) cos^2(3x)/(3cos^2x)
=lim(x→π/2) 2cos(3x)sin(3x)/(6cosxsinx)
=lim(x→π/2) cos(3x)/cosx
=lim(x→π/2) -3sin(3x)/(-sinx)
=9

x→π/2
lim tanx / tan3x
=lim sinx/sin3x * lim cos3x/cosx
=-lim cos3x/cosx
该极限为0/0型,根据L'Hospital法则
=-lim (cos3x)' / (cosx)'
=-lim 3sin3x / sinx
=3
有不懂欢迎追问