Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院极限存在准则证第六节 极限存在准则 两个重要极限Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院上两式同时成立,上述数列极限存在的准则可以推广到函数的极限Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院准则 I和准则 I称为夹逼准则.作为准则 的应用,下面证明一个重要的极限:Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院(1)证明两个重要极限Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院例11 求Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院解例12 求解 原式Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院例13 求 解2.单调有界准则单调增加 单调数列单调减少Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院几何解释:Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院图1-30Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院类似地,Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院可以证明,Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院例14 求解 原式柯西极限存在准则Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院证明 必要性所以这条件是必要的.Yibin UniversityTeaching Plan on Advanced Mathematics宜宾学院充分性的证明请同学们自己证明返回