托马斯微积分课件1.4-Continuity.ppt

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1、Chapter1LimitsandContinuity1.3LimitsInvolvingInfinity1.1RatesofChangeandLimits1.2FindingLimitsandOne-SidedLimits1.4Continuity1.5TangentLines1.4Continuity1.4.1ContinuityataPoint1.4.2ContinuousFunctionsAlgebraicCombinationsComposites1.4.3IntermediateValueTheore

2、mforContinuousFunctions1.4.1ContinuityataPointLetusrecallthemethodtographarealfunction.作业请抄上题目Left-continuousRight-continuousClassificationforthepointofdiscontinuityThefirstkind:及均存在,若称若称Thesecondkind:及中至少一个不存在,称若其中有一个为振荡,称若其中有一个为为可去间断点.为跳跃间断点.为无穷间断点.为振荡间断点.为

3、其无穷间断点.为其振荡间断点.为可去间断点.例如:显然为其可去间断点.(4)(5)为其跳跃间断点.1.4.2ContinuousFunctionsAlgebraicCombinationsComposites任意初等函数在其定义区间是连续的。例：设时提示:为连续函数.1.4.3IntermediateValueTheoremforContinuousFunctionsSomeresultsfortheboundednessofafunction.例.证明方程一个根.证:显然又故据零点定理,至少存在一点使即说明:内

4、必有方程的根;取的中点内必有方程的根;可用此法求近似根.二分法在区间内至少有则则内容小结ExercisesP1325,6,9,13,20,21,24;P13328(a),34,37.