lim趋近于无穷大(x+1分子x-1)的x次方

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lim趋近于无穷大(x+1分子x-1)的x次方

lim[(x-1)/(x+1)]^x
=lim[1-2/(x+1)]^x
=lim[1-2/(x+1)]^[-(x+1)/2*(-2)]/[1-2/(x+1)]
limx趋近于无穷大[1-2/(x+1)]=1
原式
={lim[1-2/(x+1)]^[-(x+1)/2]}^(-2)
=e^(-2)
=1/e²