limx→1{√(5x-4)-√x}/(x-1)的值

问题描述:

limx→1{√(5x-4)-√x}/(x-1)的值

limx→1{√(5x-4)-√x}/(x-1)
=limx→1{√(5x-4)-√x}{√(5x-4)+√x}/(x-1){√(5x-4)+√x}
=limx→1(4x-4)/(x-1){√(5x-4)+√x}
=4lim(x→1)1/{√(5x-4)+√x}
=4/2=2