求lim(x→1)(X^1/3-1)/(x^1/2-1)
问题描述：
求lim(x→1)(X^1/3-1)/(x^1/2-1)
不用洛比塔法则,坐等
答
令a=x^1/6
则a趋于1
所以原式=lim(a²-1)/(a³-1)
=lim(a-1)(a+1)/(a-1)(a²+a+1)
=lim(a+1)/(a²+a+1)
=2/3