分类：教育/科学-理工学科-数学
问题：高数lim(x→∞)[(3+x)/(6+x)]^[(x
lim(x→∞)[(3+x)/(6+x)]^[(x-1)/2]
回答：原式=lim(x→∞)[(6+x-3)/(6+x)]^[(x-1)/2]
=lim(x→∞){[1-(3/6+x)]^[(6+x)/(-3)]}^{[-3/(6+x)]*[(x-1)/2]}
=e^lim(x→∞)[-3/(6+x)]*[(x-1)/2]
=e^lim(x→∞)[(-3/2)*(x-1)/(6+x)]
=e^(-3/2).