求极限,大侠无敌x趋近于无穷大,lim[(3x+4)/(3x-1)]^(x+1)的极限怎么求?

Question

求极限,大侠无敌
x趋近于无穷大,lim[(3x+4)/(3x-1)]^(x+1)的极限怎么求?

Answer 1

【以下默认x→∞】
lim[(3x+4)/(3x-1)]^(x+1)
=lim[1+5/(3x-1)]^(x+1)
=lim{1+1/[(3x-1)/5]}^{[(3x-1)/5]×(5/3)+(4/3)}
=lim{1+1/[(3x-1)/5]}^{[(3x-1)/5]×(5/3)}×lim{1+1/[(3x-1)/5]}^(4/3)
=lim^(5/3)×1
=e^(5/3)