⑩天掌 Teaching Plan on Advanced Mathematics 第六节极限存在准则两个重要极限 极限存在准则 准则|如果数列xn,Jn及乙满足下列条件: (1)yn≤xn≤zn(=1,2,3…) (2)lim yn=a, liman =a, n→00 那末数列xn的极限存在,且 limx=a 证∵yn→>a,zn→a," VE>0,N1>0,N2>0,使得 当n>N时恒有yn-a<E, 当n>N时恒有zn-a<E,Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 极限存在准则 准则Ⅰ 如果数列 n n x , y 及 n z 满足下列条件: (2) lim , lim , (1) ( 1,2,3 ) y a z a y x z n n n n n n n n = = = → → 那末数列xn的极限存在, 且 xn a n = → lim . 证 y a, z a, n → n → 0, N1 0, N2 0, 使得, 1 n N y − a 当 时恒有 n , 2 n N z − a 当 时恒有 n 第六节 极限存在准则 两个重要极限