当x≥1时,有[xl≤x≤[xl+1, 十 )≤(+)≤(1+ x]+1 而im(1+,,)=mim(×、1yxl.im(1+ x→+0 x→+0 im(1+,,,)x →+0 x|十 lim(1+ lim(1+ x→+0 x]+1 x→+0 x]+1 lim(1+ x→+0当 x  1时, 有[x]  x  [x]+ 1, ) , [ ] 1 ) (1 1 ) (1 [ ] 1 1 (1 [ ] [ ]+1  +  + + + x x x x x x ) [ ] 1 ) lim (1 [ ] 1 ) lim (1 [ ] 1 lim (1 [ ] 1 [ ] x x x x x x x x + = +  + →+  →+  + →+  而 = e, [ ] 1 1 [ ] ) [ ] 1 1 ) lim (1 [ ] 1 1 lim (1 ) [ ] 1 1 lim (1 − →+  + →+  →+  +  + + = + + + x x x x x x x x = e, ) . 1 lim (1 e x x x  + = →+ 