微积分中若干问题的研究(Ⅰ)  

Study on the Mang Questions of the Calculus ( I )

作　　者：侯双根[1] 

机构地区：[1]安阳大学,河南安阳455000

出　　处：《安阳大学学报（综合版）》2004年第1期52-58,共7页

摘　　要：对于复合函数的求导法则,给出一种令人信服的严格的完整证明(其它教材中的证明均不完整或证明不能令人满意;明确了∞-∞型的未定式定义,并给出了该未定式化为0/0型或∞/∞型的未定式的理论依据;利用两个推广定理证明了弱条件下不定积分的分部积分公式及变上限的定积分所确定的函数的奇偶性。In the first question, a convincing and strict proof is given to the derivation principle of the compound functions . In other books, some proofs are not complete, such as [l],[2],[3], and some proofs are not satisfactory, such as [4], [5] , [6], [7] , [8]. In the second question, three simple ways of proving (In I x I )' = 1/x are given. In the third question, what the undetermined form ∞ - ∞ is explained and the base of the theory that is applied to change this form to 0/0 or ∞ / ∞ . In the fourth question, a new way of working out local maximum or local minimum of a variable function is given. In the fifth question, two generalized theorems, such as [9] ,[10], is applied to prove the formula of integration by parts of the indefinite integral which is restricted by less conditions and the odd or even functions which are determined by definite integral with variable upper limit.

关 键 词：微积分 复合函数 求导法则 极值 分部积分公式 

分 类 号：O172[理学—数学]