求x趋近于1时,lim立方根x^2-2立方根x+1/(x-1)^2

题目

求x趋近于1时,lim立方根x^2-2立方根x+1/(x-1)^2

答案

用洛必达法测 分子分母同时求导
lim立方根x^2-2立方根x+1/(x-1)^2
=lim立方根x^2-lim2立方根x+lim1/(x-1)^2
=1-2+无穷大=无穷大
题目怎么看都觉得怪 目测你少打了中括号导致我理解错误
lim[立方根x^2-2立方根x+1] / (x-1)^2
=lim [2/3 x^(-1/3) - 2/3 x^(-2/3)] / (2x-2)
=lim [-2/9 x^(-4/3) + 4/9 x^(-5/3)] / 2
=[-2/9 + 4/9] /2
=1/9