求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))

题目

求极限 lim n->1 ((x^1/3-1)/(x^1/2-1))

答案

用洛比塔法则
/lim_{x -> 1} ((x^1/3-1)/(x^1/2-1)) = /lim_{x -> 1} ((x^1/3-1)'/(x^1/2-1)') =
/lim_{x -> 1} (2 * x ^(-1/6) / 3) = 2 / 3