求极限lim [x^(n+1)-(n+1)x+n]/(x-1)^2 x趋于1
人气：446 ℃ 时间：2020-04-08 23:35:29
解答
lim(x->1)(x^(n+1)-(n+1)x+n)/(x-1)^2=lim(x->1)(x^(n+1)-(n+1)x+n)'/((x-1)^2)'=lim(x->1)((n+1)x^n-(n+1))/(2(x-1))=lim(x->1)((n+1)x^n-(n+1))'/(2(x-1))'=lim(x->1)(n(n+1)x^(n-1))/(2x)=n(n+1)/2
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