求极限:lim(x→1)根号5x-4-根号x/x-1是(√(5x-4)-√x)/x-1
问题描述:
求极限:lim(x→1)根号5x-4-根号x/x-1
是(√(5x-4)-√x)/x-1
答
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
答
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!