⑩天掌 Teaching Plan on Advanced Mathematics 当x≥1时,有[x]≤xs|x+1, ≤(1+-)≤(1+ lx]+1 x+ 而im(1+ x]+1 im(1+ 1 xl. lim(1+ x→+0 x→+0 im(1+ x]+1 im(1+ x]+1 lim(1+ x→+0 x→+0 x]+1 lim(1+-)2=e x→+0Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 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 [ ] 1 1 [ ] ) [ ] 1 1 ) lim (1 [ ] 1 1 lim (1 ) [ ] 1 1 lim (1 − →+  + →+  →+  +  + + = + + + x x x x x x x x ) . 1 lim (1 e x x x  + = →+ 