求lim(1-x/2)^2/x x趋近与0的极限 求lim(1-x)^1/3x x趋近与0的极限

题目

求lim(1-x/2)^2/x x趋近与0的极限 求lim(1-x)^1/3x x趋近与0的极限

答案

令 x/2 = - t ,t->0
那么化为(1+t) ^(-1/t) = 1 / [ (1+t)^(1/t) ] = 1/e
(1-x)^1/3x = (1-x)^(1/x)^(1/3) = 1/e^(1/3)