calc i complete

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calculus 1

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  • CALCULUSI PaulDawkins
  • Calculus I 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface........................................................................................................................................... iii Outline........................................................................................................................................... iv Review............................................................................................................................................. 2 Introduction.............................................................................................................................................. 2 Review:Functions ................................................................................................................................... 4 Review:InverseFunctions.................................................................................................................... 10 Review:TrigFunctions ......................................................................................................................... 17 Review:SolvingTrigEquations............................................................................................................ 24 Review:SolvingTrigEquationswithCalculators,PartI .................................................................... 33 Review:SolvingTrigEquationswithCalculators,PartII................................................................... 44 Review:ExponentialFunctions ............................................................................................................ 49 Review:LogarithmFunctions............................................................................................................... 52 Review:ExponentialandLogarithmEquations.................................................................................. 58 Review:CommonGraphs...................................................................................................................... 64 Limits............................................................................................................................................ 76 Introduction............................................................................................................................................ 76 RatesofChangeandTangentLines ...................................................................................................... 78 TheLimit................................................................................................................................................. 87 OneSidedLimits .................................................................................................................................... 97 LimitProperties.....................................................................................................................................103 ComputingLimits ..................................................................................................................................109 InfiniteLimits ........................................................................................................................................117 LimitsAtInfinity,PartI.........................................................................................................................126 LimitsAtInfinity,PartII .......................................................................................................................135 Continuity...............................................................................................................................................144 TheDefinitionoftheLimit....................................................................................................................151 Derivatives.................................................................................................................................. 166 Introduction...........................................................................................................................................166 TheDefinitionoftheDerivative ...........................................................................................................168 InterpretationsoftheDerivative .........................................................................................................174 DifferentiationFormulas ......................................................................................................................179 ProductandQuotientRule ...................................................................................................................187 DerivativesofTrigFunctions ...............................................................................................................193 DerivativesofExponentialandLogarithmFunctions ........................................................................204 DerivativesofInverseTrigFunctions..................................................................................................209 DerivativesofHyperbolicFunctions....................................................................................................215 ChainRule ..............................................................................................................................................217 ImplicitDifferentiation .........................................................................................................................227 RelatedRates .........................................................................................................................................236 HigherOrderDerivatives......................................................................................................................250 LogarithmicDifferentiation..................................................................................................................255 Applications of Derivatives....................................................................................................... 258 Introduction...........................................................................................................................................258 RatesofChange......................................................................................................................................260 CriticalPoints.........................................................................................................................................263 MinimumandMaximumValues...........................................................................................................269 FindingAbsoluteExtrema ....................................................................................................................277 TheShapeofaGraph,PartI..................................................................................................................283 TheShapeofaGraph,PartII ................................................................................................................292 TheMeanValueTheorem.....................................................................................................................301 Optimization ..........................................................................................................................................308 MoreOptimizationProblems ...............................................................................................................322
  • Calculus I 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx IndeterminateFormsandLHospitalsRule........................................................................................336 LinearApproximations .........................................................................................................................342 Differentials ...........................................................................................................................................345 NewtonsMethod...................................................................................................................................348 BusinessApplications ...........................................................................................................................353 Integrals...................................................................................................................................... 359 Introduction...........................................................................................................................................359 IndefiniteIntegrals................................................................................................................................360 ComputingIndefiniteIntegrals ............................................................................................................366 SubstitutionRuleforIndefiniteIntegrals............................................................................................376 MoreSubstitutionRule .........................................................................................................................389 AreaProblem.........................................................................................................................................402 TheDefinitionoftheDefiniteIntegral.................................................................................................412 ComputingDefiniteIntegrals ...............................................................................................................422 SubstitutionRuleforDefiniteIntegrals................................................................

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