lim[(x^m-1)-(x^n-1)]/[(x^m-1) (x^n-1)]

如题所述

lim[(x^m-1)-(x^n-1)]/[(x^m-1) (x^n-1)]
=lim[(1-1/x^(m+n))-(1-1/x^(m+n))]/[(1-1/x^m) (1-1/x^n)]
=[(1-0)-(1-0)]/[(1-0) (1-0)]
=[(1-1)]/[(1) (1)]
=0/1
=0
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