lim(x趋向于1)[x/(1-x)-1/lnx]

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 10:50:02

lim(x趋向于1)[x/(1-x)-1/lnx]
lim(x趋向于1)[x/(1-x)-1/lnx]

lim(x趋向于1)[x/(1-x)-1/lnx]
原式= lim(x->1) [ x lnx - (1-x)] / [(1-x) lnx] 令t =1-x
= lim(x->1) [ x lnx - (1-x)] / - (x-1)² 等价无穷小 ln(1+ x -1) x-1
= lim(x->1) (lnx + 1 + 1) / [-2(x-1)] 洛必达法则
= ∞
lim(x->1)[x/(x-1)- 1/ lnx]
= lim(x->1) [ x lnx - (x-1)] / [(x-1) lnx] 令t =1-x
= lim(x->1) [ x lnx - (x-1)] / (x-1)² 等价无穷小 ln(1+ x -1) x-1
= lim(x->1) (lnx + 1 - 1) / [2(x-1)] 洛必达法则
= lim(x->1) (1/x) / 2 洛必达法则
= 1/2

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