im(1+)x=e,lin[1+a(x)]x(x)=e(a(x)>0) x→>0X 例3求lm(1--) x→00 解令仁=x,则x→>∞时,t→>∞.于是 lim(1-x=lim(1+ X EX lim(1-)x=lim(1+-x(D x→ [lim(1+-)x1=e 首页上页返回 下页结束首页 上页 返回 下页 结束 铃 解 e x x x + = → ) 1 lim (1  x e + (x) = 1 lim[1 ( ) ] a a (a(x)→0) 例 例 3 3 求 x x x ) 1 lim (1− →  令t=−x 则x →时 t → 于是 x x x ) 1 lim (1− → t t t − → = + ) 1 lim(1 e t t t 1 ) 1 (1 1 lim = + = →  x x x ) 1 lim (1− → t t t − → = + ) 1 lim(1 e t t t 1 ) 1 (1 1 lim = + = →  x x x ) 1 lim (1− → t t t − → = + ) 1 lim(1 e t t t 1 ) 1 (1 1 lim = + = →  x x x ) 1 lim (1− → t t t − → = + ) 1 lim(1 e t t t 1 ) 1 (1 1 lim = + = →  或 ( 1) ) 1 ) lim (1 1 lim (1 − − → → − − = + x x x x x x 1 1 ) ] 1 [lim (1 − − − → = − = + e x x x  或 ( 1) ) 1 ) lim (1 1 lim (1 − − → → − − = + x x x x x x 1 1 ) ] 1 [lim (1 − − − → = − = + e x x x  结束