n+1 证三记 n+1 d x 1+y →1.+ xdx 1n1≤1, n+1 +1 n n+1 0 ≤1+l n+1 n n+1 →Ⅰ≤ 2n 令n→,由夹逼定理得im「,xd=0 n→0 例4求极限 十∴ n→∞n+1n+2 n+n (2)limIn vm! n→>0dx x x I n n  + = 1 0 1 记 I dx x x n n +  + + = 1 0 1 1 1 则  +  + + = = 1 0 1 1 1 n I I x dx n n n 令n → ,由夹逼定理得 0 1 lim 1 0 = +  → dx x x n n 例4 求极限 ] 1 2 1 1 1 (1)lim[ n n n n + n + + + + → +  n n n n ! (2)lim ln → n n I  I +1 1 1 2 n+  n + n+ I I I n In 2 1   证三