Calculus Early Transcendentals, 10th Edition International .

Calculus Early Transcendentals, 10th EditionInternational Student VersionHoward Anton, Irl C. Bivens, Stephen DavisTABLE OF CONTENTS0 BEFORE CALCULUS 10.1 Functions 10.2 New Functions from Old 150.3 Families of Functions 270.4 Inverse Functions; Inverse Trigonometric Functions 380.5 Exponential and Logarithmic Functions 521 LIMITS AND CONTINUITY 671.1 Limits (An Intuitive Approach) 671.2 Computing Limits 801.3 Limits at Infinity; End Behavior of a Function 891.4 Limits (Discussed More Rigorously) 1001.5 Continuity 1101.6 Continuity of Trigonometric, Exponential, and Inverse Functions 1212 THE DERIVATIVE 1312.1 Tangent Lines and Rates of Change 1312.2 The Derivative Function 1432.3 Introduction to Techniques of Differentiation 1552.4 The Product and Quotient Rules 1632.5 Derivatives of Trigonometric Functions 1692.6 The Chain Rule 1743 TOPICS IN DIFFERENTIATION 1853.1 Implicit Differentiation 1853.2 Derivatives of Logarithmic Functions 192

3.3 Derivatives of Exponential and Inverse Trigonometric Functions 1973.4 Related Rates 2043.5 Local Linear Approximation; Differentials 2123.6 L’Hôpital’s Rule; Indeterminate Forms 2194 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 232TABLE OF CONTENTS0 BEFORE CALCULUS 10.1 Functions 10.2 New Functions from Old 150.3 Families of Functions 270.4 Inverse Functions; Inverse Trigonometric Functions 380.5 Exponential and Logarithmic Functions 521 LIMITS AND CONTINUITY 671.1 Limits (An Intuitive Approach) 671.2 Computing Limits 801.3 Limits at Infinity; End Behavior of a Function 891.4 Limits (Discussed More Rigorously) 1001.5 Continuity 1101.6 Continuity of Trigonometric, Exponential, and Inverse Functions 1212 THE DERIVATIVE 1312.1 Tangent Lines and Rates of Change 1312.2 The Derivative Function 1432.3 Introduction to Techniques of Differentiation 1552.4 The Product and Quotient Rules 1632.5 Derivatives of Trigonometric Functions 1692.6 The Chain Rule 1743 TOPICS IN DIFFERENTIATION 1853.1 Implicit Differentiation 1853.2 Derivatives of Logarithmic Functions 192

3.3 Derivatives of Exponential and Inverse Trigonometric Functions 1973.4 Related Rates 2043.5 Local Linear Approximation; Differentials 2123.6 L’Hôpital’s Rule; Indeterminate Forms 2194 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 2324.1 Analysis of Functions I: Increase, Decrease, and Concavity 2324.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 2444.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 2544.4 Absolute Maxima and Minima 2664.5 Applied Maximum and Minimum Problems 2744.6 Rectilinear Motion 2884.7 Newton’s Method 2964.8 Rolle’s Theorem; Mean-Value Theorem 3025 INTEGRATION 3165.1 An Overview of the Area Problem 3165.2 The Indefinite Integral 3225.3 Integration by Substitution 3325.4 The Definition of Area as a Limit; Sigma Notation 3405.5 The Definite Integral 3535.6 The Fundamental Theorem of Calculus 3625.7 Rectilinear Motion Revisited Using Integration 3765.8 Average Value of a Function and its Applications 3855.9 Evaluating Definite Integrals by Substitution 3905.10 Logarithmic and Other Functions Defined by Integrals 3966 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, ANDENGINEERING 4136.1 Area Between Two Curves 4136.2 Volumes by Slicing; Disks and Washers 421

6.3 Volumes by Cylindrical Shells 4326.4 Length of a Plane Curve 4386.5 Area of a Surface of Revolution 4446.6 Work 4496.7 Moments, Centers of Gravity, and Centroids 4586.8 Fluid Pressure and Force 4676.9 Hyperbolic Functions and Hanging Cables 4747 PRINCIPLES OF INTEGRAL EVALUATION 4887.1 An Overview of Integration Methods 4887.2 Integration by Parts 4917.3 Integrating Trigonometric Functions 5007.4 Trigonometric Substitutions 5087.5 Integrating Rational Functions by Partial Fractions 5147.6 Using Computer Algebra Systems and Tables of Integrals 5237.7 Numerical Integration; Simpson’s Rule 5337.8 Improper Integrals 5478 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 5618.1 Modeling with Differential Equations 5618.2 Separation of Variables 5688.3 Slope Fields; Euler’s Method 5798.4 First-Order Differential Equations and Applications 5869 INFINITE SERIES 5969.1 Sequences 5969.2 Monotone Sequences 6079.3 Infinite Series 6149.4 Convergence Tests 6239.5 The Comparison, Ratio, and Root Tests 631

9.6 Alternating Series; Absolute and Conditional Convergence 6389.7 Maclaurin and Taylor Polynomials 6489.8 Maclaurin and Taylor Series; Power Series 6599.9 Convergence of Taylor Series 6689.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 67810 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 69210.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 69210.2 Polar Coordinates 70510.3 Tangent Lines, Arc Length, and Area for Polar Curves 71910.4 Conic Sections 73010.5 Rotation of Axes; Second-Degree Equations 74810.6 Conic Sections in Polar Coordinates 75411 THREE-DIMENSIONAL SPACE; VECTORS 76711.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 76711.2 Vectors 77311.3 Dot Product; Projections 78511.4 Cross Product 79511.5 Parametric Equations of Lines 80511.6 Planes in 3-Space 81311.7 Quadric Surfaces 82111.8 Cylindrical and Spherical Coordinates 83212 VECTOR-VALUED FUNCTIONS 84112.1 Introduction to Vector-Valued Functions 84112.2 Calculus of Vector-Valued Functions 84812.3 Change of Parameter; Arc Length 85812.4 Unit Tangent, Normal, and Binormal Vectors 86812.5 Curvature 873

12.6 Motion Along a Curve 88212.7 Kepler’s Laws of Planetary Motion 89513 PARTIAL DERIVATIVES 90613.1 Functions of Two or More Variables 90613.2 Limits and Continuity 91713.3 Partial Derivatives 92713.4 Differentiability, Differentials, and Local Linearity 94013.5 The Chain Rule 94913.6 Directional Derivatives and Gradients 96013.7 Tangent Planes and Normal Vectors 97113.8 Maxima and Minima of Functions of Two Variables 97713.9 Lagrange Multipliers 98914 MULTIPLE INTEGRALS 100014.1 Double Integrals 100014.2 Double Integrals over Nonrectangular Regions 100914.3 Double Integrals in Polar Coordinates 101814.4 Surface Area; Parametric Surfaces 102614.5 Triple Integrals 103914.6 Triple Integrals in Cylindrical and Spherical Coordinates 104814.7 Change of Variables in Multiple Integrals; Jacobians 105814.8 Centers of Gravity Using Multiple Integrals 107115 TOPICS IN VECTOR CALCULUS 108415.1 Vector Fields 108415.2 Line Integrals 109415.3 Independence of Path; Conservative Vector Fields 111115.4 Green’s Theorem 112215.5 Surface Integrals 1130

15.6 Applications of Surface Integrals; Flux 113815.7 The Divergence Theorem 114815.8 Stokes’ Theorem 1158A APPENDICESA GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRASYSTEMS A1B TRIGONOMETRY REVIEW A13C SOLVING POLYNOMIAL EQUATIONS A27D SELECTED PROOFS A34ANSWERS TO ODD-NUMBERED EXERCISES A45INDEX I-1WEB APPENDICES (online only)4.1 Analysis of Functions I: Increase, Decrease, and Concavity 2324.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 2444.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 2544.4 Absolute Maxima and Minima 2664.5 Applied Maximum and Minimum Problems 2744.6 Rectilinear Motion 2884.7 Newton’s Method 2964.8 Rolle’s Theorem; Mean-Value Theorem 3025 INTEGRATION 3165.1 An Overview of the Area Problem 3165.2 The Indefinite Integral 3225.3 Integration by Substitution 3325.4 The Definition of Area as a Limit; Sigma Notation 3405.5 The Definite Integral 3535.6 The Fundamental Theorem of Calculus 362

5.7 Rectilinear Motion Revisited Using Integration 3765.8 Average Value of a Function and its Applications 3855.9 Evaluating Definite Integrals by Substitution 3905.10 Logarithmic and Other Functions Defined by Integrals 3966 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, ANDENGINEERING 4136.1 Area Between Two Curves 4136.2 Volumes by Slicing; Disks and Washers 4216.3 Volumes by Cylindrical Shells 4326.4 Length of a Plane Curve 4386.5 Area of a Surface of Revolution 4446.6 Work 4496.7 Moments, Centers of Gravity, and Centroids 4586.8 Fluid Pressure and Force 4676.9 Hyperbolic Functions and Hanging Cables 4747 PRINCIPLES OF INTEGRAL EVALUATION 4887.1 An Overview of Integration Methods 4887.2 Integration by Parts 4917.3 Integrating Trigonometric Functions 5007.4 Trigonometric Substitutions 5087.5 Integrating Rational Functions by Partial Fractions 5147.6 Using Computer Algebra Systems and Tables of Integrals 5237.7 Numerical Integration; Simpson’s Rule 5337.8 Improper Integrals 5478 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 5618.1 Modeling with Differential Equations 5618.2 Separation of Variables 5688.3 Slope Fields; Euler’s Method 579

8.4 First-Order Differential Equations and Applications 5869 INFINITE SERIES 5969.1 Sequences 5969.2 Monotone Sequences 6079.3 Infinite Series 6149.4 Convergence Tests 6239.5 The Comparison, Ratio, and Root Tests 6319.6 Alternating Series; Absolute and Conditional Convergence 6389.7 Maclaurin and Taylor Polynomials 6489.8 Maclaurin and Taylor Series; Power Series 6599.9 Convergence of Taylor Series 6689.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 67810 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 69210.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 69210.2 Polar Coordinates 70510.3 Tangent Lines, Arc Length, and Area for Polar Curves 71910.4 Conic Sections 73010.5 Rotation of Axes; Second-Degree Equations 74810.6 Conic Sections in Polar Coordinates 75411 THREE-DIMENSIONAL SPACE; VECTORS 76711.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 76711.2 Vectors 77311.3 Dot Product; Projections 78511.4 Cross Product 79511.5 Parametric Equations of Lines 80511.6 Planes in 3-Space 81311.7 Quadric Surfaces 821

11.8 Cylindrical and Spherical Coordinates 83212 VECTOR-VALUED FUNCTIONS 84112.1 Introduction to Vector-Valued Functions 84112.2 Calculus of Vector-Valued Functions 84812.3 Change of Parameter; Arc Length 85812.4 Unit Tangent, Normal, and Binormal Vectors 86812.5 Curvature 87312.6 Motion Along a Curve 88212.7 Kepler’s Laws of Planetary Motion 89513 PARTIAL DERIVATIVES 90613.1 Functions of Two or More Variables 90613.2 Limits and Continuity 91713.3 Partial Derivatives 92713.4 Differentiability, Differentials, and Local Linearity 94013.5 The Chain Rule 94913.6 Directional Derivatives and Gradients 96013.7 Tangent Planes and Normal Vectors 97113.8 Maxima and Minima of Functions of Two Variables 97713.9 Lagrange Multipliers 98914 MULTIPLE INTEGRALS 100014.1 Double Integrals 100014.2 Double Integrals over Nonrectangular Regions 100914.3 Double Integrals in Polar Coordinates 101814.4 Surface Area; Parametric Surfaces 102614.5 Triple Integrals 103914.6 Triple Integrals in Cylindrical and Spherical Coordinates 104814.7 Change of Variables in Multiple Integrals; Jacobians 1058

14.8 Centers of Gravity Using Multiple Integrals 107115 TOPICS IN VECTOR CALCULUS 108415.1 Vector Fields 108415.2 Line Integrals 109415.3 Independence of Path; Conservative Vector Fields 111115.4 Green’s Theorem 112215.5 Surface Integrals 113015.6 Applications of Surface Integrals; Flux 113815.7 The Divergence Theorem 114815.8 Stokes’ Theorem 1158A APPENDICESA GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRASYSTEMS A1B TRIGONOMETRY REVIEW A13C SOLVING POLYNOMIAL EQUATIONS A27D SELECTED PROOFS A34ANSWERS TO ODD-NUMBERED EXERCISES A45INDEX I-1WEB APPENDICES (online only)

6.2 Volumes by Slicing; Disks and Washers 421 6.3 Volumes by Cylindrical Shells 432 6.4 Length of a Plane Curve 438 6.5 Area of a Surface of Revolution 444 6.6 Work 449 6.7 Moments, Centers of Gravity, and Centroids 458 6.8 Fluid Pressure and Force 467 6.9 Hyperbolic Functions and H