⑩天掌 Teaching Plan on Advanced Mathematics t=-xy ∴.lim(1+-)=lim(1 lim (1+ =im(1+)-(1+)=e t-1 综上所述恒有lim(1+ e x→0 令t lim(1+x)x=lim(1+ x→>0 ∴lim(1+x)x=e 0Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 令 t = −x, t t x x x t − →−  →+   + = − ) 1 ) lim(1 1 lim (1 t t t ) 1 1 lim (1 − = + →+ ) 1 1 ) (1 1 1 lim(1 1 − + − = + − →+  t t t t = e. e x x x + = → ) 1 综上所述恒有 lim(1 , 1 x 令 t = t t x x t x ) 1 lim(1 ) lim(1 1 0 + = + → → = e. x e x x  + = → 1 0 lim(1 )