求极限:lim(x→1)根号5x-4-根号x/x-1是(√(5x-4)-√x)/x-1

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 16:58:56
求极限:lim(x→1)根号5x-4-根号x/x-1是(√(5x-4)-√x)/x-1
xQ[KA+Ӭda^h! 1ȭ-#$|RQ3ړً)BOs.s8%~}VY_qJ_¯]Tn;%;gK Hv~qXT(I% c.Yc R^W$ߨPhnמ?Mן/NŲ?p`Ls 9,AeiLzU{-S&Jӣ'OF@$ѸW2A*h:*?`')!5;%Κ[{LQVtQ_ѨX@2~.M_g,Ɍ6J8Y)yBF3Q b &LHDd KF ǁgnrX&݇͞c&/

求极限:lim(x→1)根号5x-4-根号x/x-1是(√(5x-4)-√x)/x-1
求极限:lim(x→1)根号5x-4-根号x/x-1
是(√(5x-4)-√x)/x-1

求极限:lim(x→1)根号5x-4-根号x/x-1是(√(5x-4)-√x)/x-1
lim[√(5x-4)-√x]/(x-1)
(x→1)
=
lim[√(5x-4)-√x][√(5x-4)+√x]/{[√(5x-4)+√x]*(x-1)}
(x→1)
=lim(4x-4)/{[√(5x-4)+√x]*(x-1)}
(x→1)
=lim4/[√(5x-4)+√x]
(x→1)
=4/[√(5-4)+√1]
=4/(1+1)
=2.
这个绝对是我自己做的,楼主,相信我吧,满意的话就接受吧!

lim(x→1) [√(5x-4)-√x]/(x-1)
=lim(x→1) 【[√(5x-4)-√x][√(5x-4)+√x]】/【(x-1)[√(5x-4)+√x]】,分子有理化
=lim(x→1) [(5x-4)-x]/【(x-1)[√(5x-4)+√x]】
=lim(x→1) (4x-4)/【(x-1)[√(5x-4)+√x]】
=4lim(x→1) 1/[√(5x-4)+√x]
=4*1/[√(5-4)+1]
=2

http://hi.baidu.com/wangcqqj123/blog/item/a58239163d262e5820a4e9f4.html