| 无穷限反常积分收敛时被积函数的极限状态 |
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| 引用本文： | 王庆东,庞进丽.无穷限反常积分收敛时被积函数的极限状态[J].数学学习,2013(6):1-2,20. |
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| 作者姓名： | 王庆东 庞进丽 |
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| 作者单位： | [1]商丘师范学院数学与信息科学学院,河南商丘476000 [2]商丘职业技术学院基础教学部,河南商丘476000 |
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| 基金项目： | 基金项目：国家级特色专业建设点项目（TS11575）,河南省高等教育教学改革研究省级重点项目（2012SJGLX033） |
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| 摘 要： | 根据无穷限反常积分∫a^＋∞f（x）dx收敛的柯西准则和定积分的性质，讨论被积函数f（x）当x→∞时。的极限状态，并得出当无穷限反常积分∫a^＋∞f（x）dx收敛且f（x）在a，＋∞）上连续，或者无穷限反常积分∫a^＋∞f（x）dx绝对收敛时，存在数列{xn}∩a,＋∞]且xn→＋∞（n→∞）,使limn→∞xnf（xn）=0.
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| 关 键 词： | 无穷限反常积分 收敛 柯西收敛准则 |
Limits of Integrand Functions of Convergent Improper Integrals |
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| WANG Qingdong,PANG Jinli.Limits of Integrand Functions of Convergent Improper Integrals[J].Studies In College Mathematics,2013(6):1-2,20. |
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| Authors: | WANG Qingdong PANG Jinli |
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| Institution: | 1. College of Mathematics and Information Science, Shangqiu Teacher＇s College, Shangqiu 476000, PRC; 2. Department of Basic Education, Shangqiu Vocational and Technical College, Shangqiu 476000, PRC) |
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| Abstract: | In this paper, the limit of an integrand function f（x） as x→＋ ∞） is discussed.Using Cauchy convergence criteria for improper integrals and the properties of definite integrals,we obtain the following result. If the improper integral ∫a^＋∞f（x）dx f（z）dx is convergent and f is continuous,or ifor if ∫a^＋∞f（x）dxis absolutely convergent, there exists a sequence {xn}∩a,＋∞]且xn→＋∞（n→∞）such that limx,,f （x.） = 0. |
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| Keywords: | infinite integral convergence Cauchy convergence criteria |
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