楼上的题目都写错了!
lim(x→0)（1-x/2)^[1/x+1]
=lim(x→0)（1+(-x/2))^[-2/x*(-x/2)*(x+1)/x]
=lim(x→0)[（1+(-x/2))^(-2/x)]^[-(x+1)/2]
=e^(-1/2)
=1/根号e.