讨论lim[x→0]1/[1+e^(1/x)]的极限是否存在.

Question

讨论lim[x→0]1/[1+e^(1/x)]的极限是否存在.

Answer 1

x→0+时,1/x→＋∞,e^(1/x)→＋∞,1/[1+e^(1/x)]→0
x→0-时,1/x→－∞,e^(1/x)→0,1/[1+e^(1/x)]→1
左右极限存在但不相等,所以lim(x→0)1/[1+e^(1/x)]不存在