托马斯微积分课件1.2-Finding-Limits-and-One-Sided-Limits

目录上页下页返回结束Chapter1LimitsandContinuity1.3LimitsInvolvingInfinity1.1RatesofChangeandLimits1.2FindingLimitsandOne-SidedLimits1.4Continuity1.5TangentLines目录上页下页返回结束1.2FindingLimitsandOne-SidedLimits目录上页下页返回结束1.2.1LimitRules1.2.2SandwichTheorem1.2.3One-SidedLimits目录上页下页返回结束1.2.1LimitRules目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束1.2.2SandwichTheorem目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束EXAMPLE8.FindthelimitSolution:xxxtanlim0xxxxcos1sinlim0xxxsinlim0xxcos1lim01目录上页下页返回结束EXAMPLE9.FindthelimitSolution:Bysubstitution,arcsinxtthus,sintxthereforetttsinlim0ttsin1目录上页下页返回结束20sinlimx2x2x21EXAMPLE10.FindthelimitSolution:22202sinlimxxx2121说明:计算中注意利用—————————————————————————目录上页下页返回结束nnnRππ2cossinlimRπn例11.已知圆内接正n边形面积为证明:证:nnAlimnππnnnRnAππ2cossin刘辉与烟囱……目录上页下页返回结束1.2.3One-SidedLimits目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束目录上页下页返回结束左极限与右极限左极限:0(0)fxAxfxx)(lim0,0,0当),(00xxx时,有右极限:0(0)fxAxfxx)(lim0,0,0当),(00xxx时,有目录上页下页返回结束目录上页下页返回结束谭永华667100魏志军646400目录上页下页返回结束目录上页下页返回结束EXAMPLEGiventhefunctionasfollowing:0,10,00,1)(xxxxxxfDiscusswhetherthelimitexistsornotwhenxapproachesto0SolutionDueto)(lim0xfx)1(lim0xx1)(lim0xfx)1(lim0xx1and,)0()0(fftherefore)(lim0xfxdoesnotexists.xyO11xy11xy目录上页下页返回结束Supposed)(xf,and)(lim1xfxexists,trytoevaluatethevalue.a31,121,2xxxxaEXAMPLE目录上页下页返回结束Findthevalueoffollowinglimits:目录上页下页返回结束ExercisesP1097,8,14.P11135,36.P11022,23.P11129,31.