czpx.net
当前位置:首页 >> limx趋近于π/2tAnx/tAn3x >>

limx趋近于π/2tAnx/tAn3x

求极限 当x趋向于π/2时 limtanx/tan3x 解:lim(x→π/2)tanx/tan3x =lim(x→π/2)(sinx/cosx)/(sin3x/cos3x) =lim(x→π/2)(1/cosx)/((-1)/cos3x) =-lim(x→π/2)(cos3x/cosx) =-lim(x→π/2)(-3sin3x)/(-sinx) =3

题干不完整无法作答

tanx的导数是(secx)^2,tan3x的导数是3(sec3x)^2洛比达法则要用两次原式=(1/3)*lim[(cos3x)/(cosx)]^2=(1/3)*lim[(-3sin3x)/(-sinx)]^2=3*lim{[sin(3π/2)/sin(π/2)]^2}=3

lim(x->π/2) (tanx/tan3x) (∞/∞) =lim(x->π/2) (secx)^2/[ 3(sec3x)^2] =lim(x->π/2) (cos3x)^2/[ 3(cosx)^2 ] (0/0) =lim(x->π/2) -3sin6x/( -3sin2x) =lim(x->π/2) sin6x/sin2x (0/0) =lim(x->π/2) 6cos6x/(2cos2x) =-6/(-2) =3

如有疑问,请个给我留言,请给满意,

:lim(x->π/2) (tanx/tan3x) (∞/∞) =lim(x->π/2) (secx)^2/[ 3(sec3x)^2] =lim(x->π/2) (cos3x)^2/[ 3(cosx)^2 ] (0/0) =lim(x->π/2) -3sin6x/( -3sin2x) =lim(x->π/2) sin6x/sin2x (0/0) =lim(x->π/2) 6cos6x/(2cos2x) =-6/(-2) =3

等价无穷小,从名称上看,都应该知道,是无穷小才有可能使用的方法埃 而无穷小,是指函数的极限为0的情况。 现在当x→π/2的时候,无论是tanx,还是tan3x,极限都是无穷大,不是无穷校当然不能使用等价无穷小啦。又不存在等价无穷大的玩意,数学中...

x趋于π,y=x-π趋于0, lim2tan3x/tanx =lim2tan(3y+3π)/tan(y+π) =lim2tan(3y)/tan(y) =lim2(3y)/(y) =2*3 =6

无穷/无穷 洛必达 上下同求导 lim=(tanx)' /(tan3x)' =[1/(1+x^2)]/[3/(1+(3x)^2)] =[1+9x^2]/[3(1+x^2)] 上下同除x^2 =[9+1/x^2]/[3+3/x^2]->(9+0)/(3+0)=3 所以极限为3

tan3x=tan(2x+x) =(tan2x+tanx)/(1-tan2x·tanx) =[2tanx/(1-tan²x)+tanx]/{1-[2tan²x/(1-tan²x)]} =(3tanx-tan³x)/(1-3tan²x)

网站首页 | 网站地图
All rights reserved Powered by www.czpx.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com