Anton, Bivens & Davis latest issue of Calculus Early Transcendentals Single Variable continues to build upon previous editions to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The text continues to focus on and incorporate new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students. This 10th edition retains Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level.

**BEFORE CALCULUS 1****0.1** Functions **1**

**0.2** New Functions from Old **15**

**0.3** Families of Functions **27**

**0.4** Inverse Functions; Inverse Trigonometric Functions **38**

**0.5** Exponential and Logarithmic Functions **52**

**1 LIMITS AND CONTINUITY 67**

**1.1** Limits (An Intuitive Approach) **67**

**1.2** Computing Limits **80**

**1.3** Limits at Infinity; End Behavior of a Function **89**

**1.4** Limits (Discussed More Rigorously) **100**

**1.5** Continuity **110**

**1.6** Continuity of Trigonometric, Exponential, and Inverse Functions **121**

**2 THE DERIVATIVE 131**

**2.1** Tangent Lines and Rates of Change **131**

**2.2** The Derivative Function **143**

**2.3** Introduction to Techniques of Differentiation **155**

**2.4** The Product and Quotient Rules **163**

**2.5** Derivatives of Trigonometric Functions **169**

**2.6** The Chain Rule **174**

**3 TOPICS IN DIFFERENTIATION 185**

**3.1** Implicit Differentiation **185**

**3.2** Derivatives of Logarithmic Functions **192**

**3.3** Derivatives of Exponential and Inverse Trigonometric Functions **197**

**3.4** Related Rates **204**

**3.5** Local Linear Approximation; Differentials **212**

**3.6** L’Hôpital’s Rule; Indeterminate Forms **219**

**4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 232**

**4.1** Analysis of Functions I: Increase, Decrease, and Concavity **232**

**4.2** Analysis of Functions II: Relative Extrema; Graphing Polynomials **244**

**4.3** Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents **254**

**4.4** Absolute Maxima and Minima **266**

**4.5** Applied Maximum and Minimum Problems **274**

**4.6** Rectilinear Motion **288**

**4.7** Newton’s Method **296**

**4.8** Rolle’s Theorem; Mean-Value Theorem **302**

**5 INTEGRATION 316**

**5.1** An Overview of the Area Problem **316**

**5.2** The Indefinite Integral **322**

**5.3** Integration by Substitution **332**

**5.4** The Definition of Area as a Limit; Sigma Notation **340**

**5.5** The Definite Integral **353**

**5.6** The Fundamental Theorem of Calculus **362**

**5.7** Rectilinear Motion Revisited Using Integration **376**

**5.8** Average Value of a Function and its Applications **385**

**5.9** Evaluating Definite Integrals by Substitution **390**

**5.10** Logarithmic and Other Functions Defined by Integrals **396**

**6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 413**

**6.1** Area Between Two Curves **413**

**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 Hanging Cables **474**

**7 PRINCIPLES OF INTEGRAL EVALUATION 488**

**7.1** An Overview of Integration Methods **488**

**7.2** Integration by Parts **491**

**7.3** Integrating Trigonometric Functions **500**

**7.4** Trigonometric Substitutions **508**

**7.5** Integrating Rational Functions by Partial Fractions **514**

**7.6** Using Computer Algebra Systems and Tables of Integrals **523**

**7.7** Numerical Integration; Simpson’s Rule **533**

**7.8** Improper Integrals **547**

**8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 561**

**8.1** Modeling with Differential Equations **561**

**8.2** Separation of Variables **568**

**8.3** Slope Fields; Euler’s Method **579**

**8.4** First-Order Differential Equations and Applications **586**

**9 INFINITE SERIES 596**

**9.1** Sequences **596**

**9.2** Monotone Sequences **607**

**9.3** Infinite Series **614**

**9.4** Convergence Tests **623**

**9.5** The Comparison, Ratio, and Root Tests **631**

**9.6** Alternating Series; Absolute and Conditional Convergence **638**

**9.7** Maclaurin and Taylor Polynomials **648**

**9.8** Maclaurin and Taylor Series; Power Series **659**

**9.9** Convergence of Taylor Series **668**

**9.10** Differentiating and Integrating Power Series; Modeling with Taylor Series **678**

**10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 692**

**10.1** Parametric Equations; Tangent Lines and Arc Length for Parametric Curves **692**

**10.2** Polar Coordinates **705**

**10.3** Tangent Lines, Arc Length, and Area for Polar Curves **719**

**10.4** Conic Sections **730**

**10.5** Rotation of Axes; Second-Degree Equations **748**

**10.6** Conic Sections in Polar Coordinates **754**

**A APPENDICES**

**A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS A1**

**B TRIGONOMETRY REVIEW A13**

**C SOLVING POLYNOMIAL EQUATIONS A27**

**D SELECTED PROOFS A34**

ANSWERS TO ODD-NUMBERED EXERCISES **A45**

INDEX **I-1**

**WEB APPENDICES (online only)**

Available for download atwww.wiley.com*/*college*/*anton or atwww.howardanton.com and in *WileyPLUS*.

**E REAL NUMBERS, INTERVALS, AND INEQUALITIES**

**F ABSOLUTE VALUE**

**G COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS**

**H DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS**

**I EARLY PARAMETRIC EQUATIONS OPTION**

**J MATHEMATICAL MODELS**

**K THE DISCRIMINANT**

**L SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS**

**WEB PROJECTS: Expanding the Calculus Horizon (online only)**

Available for download atwww.wiley.com*/*college*/*anton or atwww.howardanton.com and in *WileyPLUS*.

**COMET COLLISION ITERATION AND DYNAMICAL SYSTEMS RAILROAD DESIGN ROBOTICS**