Question

求极限！

手机输入不好，麻烦各位了！
limX趋于无穷大(X/1+X)^(X+2)最好有点过程，不会这类的！

Answer 1

lim（x趋于无穷大）[x/(1+x)^(x+2)
=lim(x趋于无穷大）（x+1-1）/(x+1)]^(x+2)
=lim（x趋于无穷大）[1+1/(-x-1)]^[(-x-1)(-1)+1]
=e^(-1)lim（x趋于无穷大）[1+(-1)/(x+1)]
=e^(-1)(1+lim（x趋于无穷大）[(-1/x)/(1+1/x)
=e^(-1)(1+0)
=e^(-1)