lim(x+2)/(x-2)^x/3 当x趋于无穷大时怎么算呀?
问题描述：
lim(x+2)/(x-2)^x/3 当x趋于无穷大时怎么算呀?
答
答：
lim(x→∞) { [(x+2)/(x-2)]^(x/3) }
=lim(x→∞) { [1+4/(x-2)]^[(x-2+2)/4*(4/3)] }
=lim(x→∞) { [1+4/(x-2)]^[x-2)/4] }^(4/3) * { [1+4/(x-2) ]^(2/3)
=e^(4/3)