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Chapter1Functions函数
1.Definition1AfunctionfisarulethatassignstoeachelementxinasetAexactlyoneelementcalledfxinasetB.2ThesetAiscalledthedo__in定义域ofthefunction.3Therange值域offisthesetofallpossiblevaluesoffxasxvariesthroughoutthedo__in.
2.BasicElementaryFunctions基本初等函数1constantfunctionsfx=c2powerfunctions3exponentialfunctionsdo__in:Rrange:4logarithmicfunctionsdo__in:range:R5trigonometricfunctionsfx=sinxfx=cosxfx=tanxfx=cotxfx=secxfx=cscx6inversetrigonometricfunctionsdo__inrangegraphfx=arcsinxorfx=arccosxorfx=arctanxorRfx=arccotxorR
3.DefinitionGiventwofunctionsfandgthecompositefunction复合函数isdefinedbyNoteExampleIffindeachfunctionanditsdo__in.
4.DefinitionAnelementaryfunction初等函数isconstructedusingcombinationsaddition加subtraction减multiplication乘division除andcompositionstartingwithbasicelementaryfunctions.Exampleisanelementaryfunction.isanelementaryfunction.1Polynomial多项式Functionswherenisanonnegativeinteger.Theleadingcoefficient系数Thedegreeofthepolynomialisn.Inparticular特别地TheleadingcoefficientconstantfunctionTheleadingcoefficientlinearfunctionTheleadingcoefficientquadratic二次functionTheleadingcoefficientcubic三次function2Rational有理FunctionswherePandQarepolynomials.3RootFunctions
4.Pie__wiseDefinedFunctions分段函数
5.
6.Properties性质1Symmetry对称性evenfunction:initsdo__in.sthey-axis.oddfunction:initsdo__in.symmetricabouttheorigin.2monotonicity单调性Afunctionfiscalledincreasingoninterval区间IifItiscalleddecreasingonIif3boundedness有界性4periodicity周期性Examplefx=sinxChapter2LimitsandContinuity
1.DefinitionWewriteandsay“fxapproachestendsto趋向于Lasxtendstoa”ifwecan__kethevaluesoffxarbitrarily任意地closetoLbytakingxtobesufficiently足够地closetoaoneithersideofabutnotequaltoa.Notemeansthatinfindingthelimitoffxasxtendstoaweneverconsiderx=a.Infactfxneednotevenbedefinedwhenx=a.Theonlythingthat__ttersishowfisdefinedneara.
2.LimitLawsSupposethatcisaconstantandthelimit___ist.ThenNoteFrom2weh__e
3.12Note
4.One-SidedLimits1left-handlimitDefinitionWewriteandsay“fxtendstoLasxtendstoafromleft”ifwecan__kethevaluesoffxarbitrarilyclosetoLbytakingxtobesufficientlyclosetoaandxlessthana.2right-handlimitDefinitionWewriteandsay“fxtendstoLasxtendstoafromright”ifwecan__kethevaluesoffxarbitrarilyclosetoLbytakingxtobesufficientlyclosetoaandxgreaterthana.
5.TheoremSolutionSolution
6.Infinitesi__ls无穷小量andinfinities无穷大量1DefinitionWesayfxisaninfinitesi__lasissomenumberorExample1isaninfinitesi__lasExample2isaninfinitesi__las2Theoremandgxisbounded.NoteExample3DefinitionWesayfxisaninfinityasissomenumberorExample1isaninfinityasExample2isaninfinityas4TheoremNotemnarenonnegativeinteger.Exercises。