望采纳，关键是分子分母趋于0的元素消掉
这个题考一个公式，当然也可以用洛必达法则做
用罗必塔法则得
原式 = lim
= lim
1-x^(1/2) = 1^3- [x^(1/6)]^3 = [1-x^(1/6)]. [ 1+x^(1/6) +x^(1/3) ]
1-x^(1/3) = 1^2- [x^(1/6)]^2 = [1-x^(1/6)]. [ 1+x^(1/6) ]
lim(x->1) [1-x^(1/2) ]/[1-x^(1/3) ]
=lim(x->1) [1-x^(1/6)]. [ 1+x^(1/6) +x^(1/3) ]/ { [1-x^(1/6)]. [ 1+x^(1/6)] }
=lim(x->1) [ 1+x^(1/6) +x^(1/3) ]/ [ 1+x^(1/6)]
=3/2
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