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 is convergent and f is continuous ,or if∫+∞a f (x)d x is absolutely convergent ,there exists a sequence{xn} ⊂[a ,+ ∞) with xn → + ∞(n → ∞) such that limn→ ∞xn f (xn ) = 0 .%＋∞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）d x收敛且 f （x）在[a ，＋∞）上连续，或者无穷限反常积分a f （x）d x绝对收敛时，存在数列｛xn｝⊂[a ，＋∞）且 xn →＋∞（n →∞），使limn→∞xn f （xn ）＝0．＋∞∫
展开▼
