im(1+-)=e,lin[1+a(x)](x)=e(a(x)->0) x→00 例3求lm(1--)x x→∞0 解令-x,则x→>∞时,t→>∞.于是 lim(1-)x=lim(1+-1=lim x→00 t→∞ (1+)y Ei lim(1-)x=lim(1+)-x(-1 x→00 x→)00 [lim(1+-)-x 页返回 下页结束 铃首页 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