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

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

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

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