lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限

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lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限

lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限
lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限

lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限
为了简便,设1/t=-3/(x+6),则x=-3t-6
lim(x→∞)[(3+x)/(6+x)]^[(x-1)/2]
=lim[1-3/(x+6)]^[(x-1)/2]
=lim(1+1/t)^[(-3t-7)/2]
=lim1/[(1+1/t)^t)^(3/2)]*(1+1/t)^(-7/2)
=1/e^(3/2)