Preface | p. ix |

Functions | p. 1 |

Functions and Their Graphs | p. 1 |

Combining Functions; Shifting and Scaling Graphs | p. 14 |

Trigonometric Functions | p. 22 |

Exponential Functions | p. 30 |

Inverse Functions and Logarithms | p. 36 |

Graphing with Calculators and Computers | p. 50 |

Limits and Continuity | p. 55 |

Rates of Change and Tangents to Curves | p. 55 |

Limit of a Function and Limit Laws | p. 62 |

The Precise Definition of a Limit | p. 74 |

One-Sided Limits and Limits at Infinity | p. 84 |

Infinite Limits and Vertical Asymptotes | p. 97 |

Continuity | p. 103 |

Tangents and Derivatives at a Point | p. 115 |

Questions to Guide Your Review | p. 119 |

Practice Exercises | p. 120 |

Additional and Advanced Exercises | p. 122 |

Differentiation | p. 125 |

The Derivative as a Function | p. 125 |

Differentiation Rules for Polynomials, Exponentials, Products, and Quotients | p. 134 |

The Derivative as a Rate of Change | p. 146 |

Derivatives of Trigonometric Functions | p. 157 |

The Chain Rule and Parametric Equations | p. 164 |

Implicit Differentiation | p. 177 |

Derivatives of Inverse Functions and Logarithms | p. 183 |

Inverse Trigonometric Functions | p. 194 |

Related Rates | p. 201 |

Linearization and Differentials | p. 209 |

Hyperbolic Functions | p. 221 |

Questions to Guide Your Review | p. 227 |

Practice Exercises | p. 228 |

Additional and Advanced Exercises | p. 234 |

Applications of Derivatives | p. 237 |

Extreme Values of Functions | p. 237 |

The Mean Value Theorem | p. 245 |

Monotonic Functions and the First Derivative Test | p. 254 |

Concavity and Curve Sketching | p. 260 |

Applied Optimization | p. 271 |

Indeterminate Forms and L'Hopital's Rule | p. 283 |

Newton's Method | p. 291 |

Antiderivatives | p. 296 |

Questions to Guide Your Review | p. 306 |

Practice Exercises | p. 307 |

Additional and Advanced Exercises | p. 311 |

Integration | p. 315 |

Estimating with Finite Sums | p. 315 |

Sigma Notation and Limits of Finite Sums | p. 325 |

The Definite Integral | p. 332 |

The Fundamental Theorem of Calculus | p. 345 |

Indefinite Integrals and the Substitution Rule | p. 354 |

Substitution and Area Between Curves | p. 360 |

The Logarithm Defined as an Integral | p. 370 |

Questions to Guide Your Review | p. 381 |

Practice Exercises | p. 382 |

Additional and Advanced Exercises | p. 386 |

Applications of Definite Integrals | p. 391 |

Volumes by Slicing and Rotation About an Axis | p. 391 |

Volumes by Cylindrical Shells | p. 401 |

Lengths of Plane Curves | p. 408 |

Areas of Surfaces of Revolution | p. 415 |

Exponential Change and Separable Differential Equations | p. 421 |

Work | p. 430 |

Moments and Centers of Mass | p. 437 |

Questions to Guide Your Review | p. 444 |

Practice Exercises | p. 444 |

Additional and Advanced Exercises | p. 446 |

Techniques of Integration | p. 448 |

Integration by Parts | p. 448 |

Trigonometric Integrals | p. 455 |

Trigonometric Substitutions | p. 461 |

Integration of Rational Functions by Partial Fractions | p. 464 |

Integral Tables and Computer Algebra Systems | p. 471 |

Numerical Integration | p. 477 |

Improper Integrals | p. 487 |

Questions to Guide Your Review | p. 497 |

Practice Exercises | p. 497 |

Additional and Advanced Exercises | p. 500 |

Infinite Sequences and Series | p. 502 |

Sequences | p. 502 |

Infinite Series | p. 515 |

The Integral Test | p. 523 |

Comparison Tests | p. 529 |

The Ratio and Root Tests | p. 533 |

Alternating Series, Absolute and Conditional Convergence | p. 537 |

Power Series | p. 543 |

Taylor and Maclaurin Series | p. 553 |

Convergence of Taylor Series | p. 559 |

The Binomial Series | p. 569 |

Questions to Guide Your Review | p. 572 |

Practice Exercises | p. 573 |

Additional and Advanced Exercises | p. 575 |

Polar Coordinates and Conics | p. 577 |

Polar Coordinates | p. 577 |

Graphing in Polar Coordinates | p. 582 |

Areas and Lengths in Polar Coordinates | p. 586 |

Conic Sections | p. 590 |

Conics in Polar Coordinates | p. 599 |

Conics and Parametric Equations; The Cycloid | p. 606 |

Questions to Guide Your Review | p. 610 |

Practice Exercises | p. 610 |

Additional and Advanced Exercises | p. 612 |

Appendices | p. AP-1 |

Real Numbers and the Real Line | p. AP-1 |

Mathematical Induction | p. AP-7 |

Lines, Circles, and Parabolas | p. AP-10 |

Trigonometry Formulas | p. AP-19 |

Proofs of Limit Theorems | p. AP-21 |

Commonly Occurring Limits | p. AP-25 |

Theory of the Real Numbers | p. AP-26 |

The Distributive Law for Vector Cross Products | p. AP-29 |

The Mixed Derivative Theorem and the Increment Theorem | p. AP-30 |

Answers | p. A-1 |

Index | p. I-1 |

A Brief Table of Integrals | p. T-1 |

Credits | p. C-1 |

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