**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**