Question

limx→1 {[x^(1/3)]-1}/{[x^(1/2)]-1}的极限多少

Answer 1

令 x=t^6 ,由 x 趋于 1 得 t 趋于 1 ,

原式 = lim(t→1) [(t^2-1)/(t^3-1)]

= lim(t→1) [(t+1)(t-1)] / [(t-1)(t^2+t+1)]

= lim(t→1) (t+1)/(t^2+t+1)

= (1+1)/(1+1+1)

= 2/3