limx趋近于无穷 (x+1/x+2)^x+3的极限
问题描述：
limx趋近于无穷 (x+1/x+2)^x+3的极限
答
lim[(x+1)/(x+2)]^(x+3)
=lim[(x+2-1)/(x+2)]^(x+3)
=lim{1-[1/(x+2)]}^(x+3)
=lim【{1+[-1/(x+2)]}^[-(x+2)]】^[-(x+3)/(x+2)]
=e^lim[-(x+3)/(x+2)]
=e^(-1)
=1/e