1、 cI|:1004- 3888(2002) 02- 0170- 03Kl K+ZEX郑文杰( B S,6 445000)K 1:在微积分中,极限是最重要的概念之一,而且微分a积分a级数等概念都是由极限来定义的b因此,掌握好用极限定义证明部分极限问题的方法大有必要,从极限定义证明极限的方法的特点加以分析,可归纳总结出放大法a乘方法a取点法a夹逼法和反证法等5种方法b1oM:极限;定义;证明方法ms |: O172 DS M : A1 Kll1: !X n B , A B , E,9i B1 N , Pn N H,X n- A XB Mxf f ( x ) Tf ( x )- A 0,9iD 0,
2、 aT0 1 1: 7a 1n- 1= A,5A 0,u m Twa= (1+ A) n 1+ nA= 1+ n( a 1n- 1)a 1n- 1 a- 1nPE 0,9vN ( |N = a- 1E ) ,5n N H,a 1n- 1 1)2. 2 ZEZE1 |f K 5,i O M xB t0,N K5 n5A|f |YVZ , Kl ZE) K5b2 limx y0 5 x = 0 :PE 0,1 P5 x - 0 = 5 x 0,1 Px 2- 4 1 H, n n 1,:an= n n= 1+ hn( hn 0) ,5n= ( 1+ hn ) n= 1+ nhn+ n( n- 1)
3、2 h2n+,+ hnn n ( n- 1)2 h2n0 hn 2n- 1 1 an= 1+ hn 1+ 2n- 1/limn y (1+ 2n- 1)= 1PE 0,1 P1+ 2n- 1- 1 = 2n- 1 2E2+ 1|N = 2E2 + 1 ,n N H,1+ 2n- 1- 1 N 1B Mx n, Tx n- a N 2B Mx n , Tx n- b N H, ( 1)1712 :Kl K+ZET#(2) T H ,(1) Tx n a+ b2 , b +ZE,l K5n, , 85i“/ FZEb H,BK 5 +ZE B ,1%49,MvE1 Ll ,B ?z ,i ? ag
4、. ID: 1 华东师范大学数学系. 数学分析(第二版) M .北京:高等教育出版社,1991. 33 34, 64. 2 同济大学数学教研室.高等数学(第四版) M .北京:高等教育出版社,1996. 39.Methods of Limit Proving by Using the Definition of LimitZHEN Wen-jie( Preparatory Department, Hubei I nstitute f or N ationalities , E nshi, H ubei 445000, China )Abstract:Limit is one of the mo
5、st important concepts in calculus. Concepts such as differential calcu-lus, integral calculus and progression, are all defined by limit. So, itps rather necessary to master a few meth-ods of proving some limit problems. By analyzing the characteristics of limit proving by using the definitionof limit, five methods to prove limit, amplifying, multiplying, adopting, squeezing and disproving were con-cluded.Key words:limit; definition; prove methods172 j 2002 M
