SOLUTIONS MANUAL - THIRD EDITION William Briggs Lyle Cochran Bernh...

SOLUTIONS MANUAL

MARK WOODARD

CALCULUS

EARLY TRANSCENDENTALS

THIRD EDITION

William Briggs Lyle Cochran Bernhard Gillett Eric Schulz (For Complete File Downlink at the end of this File) 1 / 4

Contents

• Functions5

1.1 ReviewofFunctions......................................... 5 1.2 Representing Functions....................................... 14 1.3 Inverse, Exponential and Logarithmic Functions......................... 32 1.4 TrigonometricFunctionsandTheirInverses............................ 41 ChapterOneReview............................................ 54

• Limits67

2.1 TheIdeaofLimits.......................................... 67 2.2 DefinitionofaLimit......................................... 72 2.3 TechniquesforComputingLimits ................................. 87 2.4 Infinite Limits............................................ 97 2.5 Limits at Infinity...........................................106 2.6 Continuity ..............................................120 2.7 PreciseDefinitionsofLimits ....................................133 ChapterTwoReview............................................142

• Derivatives155

3.1 IntroducingtheDerivative .....................................155 3.2 TheDerivativeasaFunction....................................164 3.3 RulesofDifferentiation .......................................182 3.4 TheProductandQuotientRules..................................190 3.5 DerivativesofTrigonometricFunctions ..............................202 3.6 DerivativesasRatesofChange...................................211 3.7 TheChainRule ...........................................226 3.8 ImplicitDifferentiation .......................................240 3.9 Derivatives of Logarithmic and Exponential Functions......................258 3.10 DerivativesofInverseTrigonometricFunctions..........................270 3.11 RelatedRates ............................................279 ChapterThreeReview...........................................291

• Applications of the Derivative 307

4.1 MaximaandMinima ........................................307 4.2 MeanValueTheorem ........................................322 4.3 WhatDerivativesTellUs......................................330 4.4 GraphingFunctions .........................................348 4.5 OptimizationProblems .......................................382 4.6 LinearApproximationandDifferentials ..............................405 4.7 L’Hˆopital’sRule ...........................................415 4.8 Newton’sMethod ..........................................429 4.9 Antiderivatives............................................445 ChapterFourReview ...........................................456

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2Contents 5Integration479 5.1 Approximating Areas under Curves . . ..............................479 5.2 DefiniteIntegrals...........................................499 5.3 Fundamental Theorem of Calculus.................................519 5.4 WorkingwithIntegrals .......................................536 5.5 Substitution Rule..........................................546 ChapterFiveReview............................................557

• Applications of Integration 573

6.1 VelocityandNetChange ......................................573 6.2 RegionsBetweenCurves ......................................587 6.3 VolumebySlicing ..........................................602 6.4 VolumebyShells...........................................610 6.5 LengthofCurves...........................................620 6.6 SurfaceArea .............................................626 6.7 PhysicalApplications ........................................634 ChapterSixReview ............................................644

• Logarithmic, Exponential, and Hyperbolic Functions 661

7.1 Logarithmic and Exponential Functions Revisited........................661 7.2 ExponentialModels .........................................669 7.3 HyperbolicFunctions ........................................675 ChapterSevenReview...........................................687

• Integration Techniques693

8.1 BasicApproaches ..........................................693 8.2 IntegrationbyParts.........................................703 8.3 TrigonometricIntegrals .......................................722 8.4 Trigonometric Substitutions....................................731 8.5 PartialFractions...........................................748 8.6 IntegrationStrategies ........................................763 8.7 OtherMethodsofIntegration....................................798 8.8 NumericalIntegration........................................807 8.9 ImproperIntegrals..........................................818 ChapterEightReview ...........................................833

• Differential Equations855

9.1 BasicIdeas..............................................855 9.2 DirectionFieldsandEuler’sMethod................................861 9.3 SeparableDifferentialEquations ..................................873 9.4 SpecialFirst-OrderLinearDifferentialEquations.........................886 9.5 ModelingwithDifferentialEquations ...............................894 ChapterNineReview ...........................................903 10 Sequences and Infinite Series 911 10.1 AnOverview.............................................911 10.2 Sequences...............................................919 10.3 Infinite Series.............................................933 10.4 TheDivergenceandIntegralTests.................................944 10.5 ComparisonTests ..........................................955 10.6 AlternatingSeries ..........................................963 10.7 TheRatioandRootTests .....................................970 10.8 ChoosingaConvergenceTest....................................976 ChapterTenReview............................................993 Copyrightcff2019 Pearson Education, Inc. 3 / 4

Contents3 11 Power Series1005 11.1 ApproximatingFunctionsWithPolynomials ...........................1005 11.2 PropertiesofPowerSeries .....................................1023 11.3 TaylorSeries.............................................1032 11.4 WorkingwithTaylorSeries.....................................1047 ChapterElevenReview ..........................................1061 12 Parametric and Polar Curves 1071 12.1 ParametricEquations........................................1071 12.2 PolarCoordinates ..........................................1088 12.3 CalculusinPolarCoordinates ...................................1108 12.4 ConicSections ............................................1123 ChapterTwelveReview ..........................................1143 13 Vectors and the Geometry of Space 1161 13.1 VectorsinthePlane.........................................1161 13.2 VectorsinThreeDimensions ....................................1169 13.3 DotProducts.............................................1179 13.4 CrossProducts............................................1187 13.5 LinesandPlanesinSpace......................................1196 13.6 CylindersandQuadricSurfaces ..................................1204 ChapterThirteenReview .........................................1219 14 Vector-Valued Functions 1233 14.1 Vector-ValuedFunctions ......................................1233 14.2 CalculusofVector-ValuedFunctions................................1241 14.3 MotioninSpace ...........................................1247 14.4 LengthofCurves...........................................1266 14.5 CurvatureandNormalVectors...................................1272 ChapterFourteenReview .........................................1283 15 Functions of Several Variables 1299 15.1 GraphsandLevelCurves......................................1299 15.2 LimitsandContinuity........................................1311 15.3 PartialDerivatives..........................................1317 15.4 TheChainRule ...........................................1329 15.5 DirectionalDerivativesandtheGradient .............................1340 15.6 TangentPlanesandLinearApproximation ............................1354 15.7 Maximum/MinimumProblems...................................1362 15.8 Lagrange Multipliers.........................................1373 ChapterFifteenReview ..........................................1382 16 Multiple Integration1393 16.1 DoubleIntegralsoverRectangularRegions ............................1393 16.2 DoubleIntegralsoverGeneralRegions...............................1400 16.3 DoubleIntegralsinPolarCoordinates...............................1416 16.4 TripleIntegrals............................................1430 16.5 Triple Integrals in Cylindrical and Spherical Coordinates.................... 1442 16.6 IntegralsforMassCalculations...................................1454 16.7 ChangeofVariablesinMultipleIntegrals .............................1465 ChapterSixteenReview..........................................1477 Copyrightcff2019 Pearson Education, Inc.

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