lim(X->1)(X/lnX-1/(X一1))=?
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lim(X->1)(X/lnX-1/(X一1))=?
lim(X->1)[X/lnX-1/(X一1)]
=lim(X->1)[x(x-1)-lnx] / [(x-1)lnx] 0/0形,用洛必达
=lim(x->1) [2x-1-1/x] / [lnx-(x-1)/x]
=lim(x->1) [2x^2-x-1] / [xlnx-x+1] 0/0形,用洛必达
=lim(x->1) (4x-1) / [lnx-x*1/x-1]
=lim(x->1) (4x-1) / (lnx-2)
=(4-1)/(0-2)
=-3/2
=lim(X->1)[x(x-1)-lnx] / [(x-1)lnx] 0/0形,用洛必达
=lim(x->1) [2x-1-1/x] / [lnx-(x-1)/x]
=lim(x->1) [2x^2-x-1] / [xlnx-x+1] 0/0形,用洛必达
=lim(x->1) (4x-1) / [lnx-x*1/x-1]
=lim(x->1) (4x-1) / (lnx-2)
=(4-1)/(0-2)
=-3/2
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