求lim[ x^(n+1)-(n+1)x+n]/(x-1)^2 x-->1=lim(t->0) [ [ 1 + (n+1)t + _数学解答

求lim[ x^(n+1)-(n+1)x+n]/(x-1)^2 x-->1
=lim(t->0) [ [ 1 + (n+1)t + (n+1)n/2t^2 + o(t^2)] -(n+1)-(n+1)t + n]/t^2？不懂

人气：223 ℃　时间：2020-09-08 12:18:27

解答

①令：x = 1+t (t->0) lim(x->1) [ x^(n+1)-(n+1)x+n]/(x-1)^2=lim(t->0) [ (1+t)^(n+1)-(n+1)(1+t) + n]/t^2【二项式展开, o(t^2) 表示t^2的高阶无穷小量：（n+1)n(n-1)t^3/3! + ... + t^(n+1)】=lim(t->0) [ [...