2、概念和运用上的一个区别；其次是总结反例加强对概念的认识，主要是从无界函数、函数在一点的连续、二元函数的偏导和可微这几个方面来说明；再其次是对定理的理解，主要介绍了罗尔中值定理和拉格朗日中值定理这两个定理；再是说明反例对概念之间关系的把握，主要是分别对可导与连续、无穷大与无界量等概念之间进行了区别联系；最后简单总结了反例能有培养逆向思维的能力.关键词：数学分析；反例；作用；归纳总结15TheEffectofCounterExampleinMathematicalAnalysisAbstract：Inmathematicalanalysis, acounterexample i
3、softenusedin proofs. Therearemany mathematicalconjectureorproposition describes universalproposition, that kindofthing all havecertain properties, or aslongasaconditionismet, will cometosomesortofconclusion. When that mathematical conjecturethis difficulty, amathematicianwould tendto lookf
4、or a a counterexample, toshowthat thisconjectureisfalse. That playsanimportantrole inmathematicalanalysis.Thispaper mainlysummarizesthe counterexample to play inmathematicalanalysis. Thefirstistheexceptionstotherecognition,mainlytothecounterexampleandreductiontoabsurdityinconceptandusethem
5、toproveadifferencestepon;Thisisfollowedbyasummaryofthecounterexampletoenhanceunderstandingoftheconcept,mainlyfromtheunboundedfunction,functionandErYuanfunctionforapartialderivativeanddifferentiabilityofseveralaspectsofthisexample; then to understandtheorem, mainlyintroducedthe Rollemeanval
6、uetheoremandLagrangemeanvalue theoremand the two theorem; then explains theconceptoftherelationshipbetweenthe example grasp, mainly on betweentheconceptof derivativeandthecontinuous, infinite with anunboundedamount of difference; summarizes thecounterexample canhavetheability ofreversethin
