求lim(x→1)(X^1/3-1)/(x^1/2-1)不用洛比塔法则,坐等_数学解答

求lim(x→1)(X^1/3-1)/(x^1/2-1)
不用洛比塔法则,坐等

人气：467 ℃　时间：2020-05-02 04:54:26

解答

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