Ⅱ.1im(l+)'=e X→00 证：当x>0时，设n≤x<n+l,则 1+m)”<(1+)<(1+)*1 m0+”=im0+ e n->0 1+ 1im+分)1=1im【+)P0+]=e n>o∞ lim(1+)'=e X>+00 BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS PRESS 目录上页下页返回结束目录 上页 下页 返回 结束 Ⅱ. 证: 当 x  0 时, 设 n  x  n +1, 则 x x (1 ) 1 + 1 1 (1 ) +  + n n +  + n n (1 ) 1 1 n n n lim (1 ) 1 1 + → + lim → = n 1 1 1 (1 ) + + + n n 1 1 1 + + n = e 1 1 lim (1 ) + → + n n n lim[(1 ) 1 ] 1 n n（ 1 n ） n = + + → = e lim (1 ) e 1 + = →+ x x x