lim(n∧2)(x∧(1/n)-x∧(1/(1+n)))n无穷大

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/02 07:33:22

由题意得到,x>0
原式=lim{n^2 x^(1/(1+n))[x^(1/n(n+1)-1]} 把括号里x^(1/(n+1))提出来
=lim{[n/(n+1)] x^(1/(1+n))[x^(1/n(n+1)-x^0] / ([(1/n(n+1)]-0])}
=lim[n/(n+1)] x^(1/(1+n)) lim[(x^t-x^0)/(t-0)] t趋向于0
=lim[n/(n+1)] x^(1/(1+n)) * d(x^t)/dt [t=0]
=(x^t *lnx) [t=0]
=lnx
本题的方法,主要运用了lim(f(x1)-f(2))/(x1-x2)=f'(x2) 当x1趋向于x2

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