limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限

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limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限

limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限
limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限

limx趋于无穷大时求x[ln(x-2)-ln(x+1)]的极限
lim(x→∞) x[ln(x-2)-ln(x+1)]
=lim(x->∞) [ln(x-2)-ln(x+1)]/(1/x)
=lim(x→∞) [1/(x-2)-1/(x+1)]/(-1/x^2)
=lim(x->∞) -[(x+1-x+2)/[(x-2)(x+1)]x^2
=lim(x->∞) -3x^2/(x^2-x-2)
=-3

重要极限,lim ln(x-2/x-1)^x=lim ln((1-1/x-1)^1-x)^x/1-x=lim lne^-1=-1