lim(x趋向于正无穷)(1+x)^1/x乘以(1+1/x)^x

lim(x趋向于正无穷)(1+x)^1/x乘以(1+1/x)^x
lim(x趋向于正无穷)(1+x)^1/x乘以(1+1/x)^x

lim(x趋向于正无穷)(1+x)^1/x乘以(1+1/x)^x
(1+x)^(1/x)=1 (x趋向+∞)
(1+1/x)^x=e (x趋向+∞)
所以原式=e

x趋向于正无穷
lim (1+x)^1/x乘以(1+1/x)^x
=lim(1+x)^1/x乘以 lim (1+1/x)^x 无穷的零次幂型和1的无穷次幂型
= 1乘e
=e