求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)
问题描述：
求极限limx趋近于1,(x^1/3-1)/(x^1/2-1)
答
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 .