### Chapter 1

Functions And Limits

1.1 | Functions and Their Representations | Exercises | p.8 |

1.2 | A Catalog of Essential Functions | Exercises | p.21 |

1.3 | The Limit of a Function | Exercises | p.33 |

1.4 | Calculating Limits | Exercises | p.43 |

1.5 | Continuity | Exercises | p.54 |

1.6 | Limits Involving Infinity | Exercises | p.67 |

Chapter 1 Review (True-False Quiz) | p.70 | ||

Chapter 1 Review (Concept Check) | p.70 | ||

Chapter 1 Review (Exercises) | p.71 |

### Chapter 2

Derivatives

2.1 | Derivatives and Rates of Change | Exercises | p.80 |

2.2 | The Derivative as a Function | Exercises | p.92 |

2.3 | Basic Differentiation Formulas | Exercises | p.105 |

2.4 | The Product and Quotient Rules | Exercises | p.112 |

2.5 | The Chain Rule | Exercises | p.120 |

2.6 | Implicit Differentiation | Exercises | p.127 |

2.7 | Related Rates | Exercises | p.132 |

2.8 | Linear Approximations and Differentials | Exercises | p.138 |

Chapter 2 Review (True-False Quiz) | p.140 | ||

Chapter 2 Review (Concept Check) | p.140 | ||

Chapter 2 Review (Exercises) | p.141 |

### Chapter 3

Inverse Functions

3.1 | Exponential Functions | Exercises | p.150 |

3.2 | Inverse Functions and Logarithms | Exercises | p.161 |

3.3 | Derivatives of Logarithmic and Exponential Functions | Exercises | p.169 |

3.4 | Exponential Growth and Decay | Exercises | p.177 |

3.5 | Inverse Trigonometric Functions | Exercises | p.183 |

3.6 | Hyperbolic Functions | Exercises | p.189 |

3.7 | Indeterminate Forms and L'Hôpital's Rule | Exercises | p.197 |

Chapter 3 Review (Concept Check) | p.199 | ||

Chapter 3 Review (True-False Quiz) | p.199 | ||

Chapter 3 Review (Exercises) | p.200 |

### Chapter 4

Applications Of Differentiation

4.1 | Maximum and Minimum Values | Exercises | p.208 |

4.2 | The Mean Value Theorem | Exercises | p.215 |

4.3 | Derivatives and the Shapes of Graphs | Exercises | p.222 |

4.4 | Curve Sketching | Exercises | p.230 |

4.5 | Optimization Problems | Exercises | p.238 |

4.6 | Newton's Method | Exercises | p.245 |

4.7 | Antiderivatives | Exercises | p.252 |

Chapter 4 Review (Concept Check) | p.253 | ||

Chapter 4 Review (Exercises) | p.254 | ||

Chapter 4 Review (True-False Quiz) | p.254 |

### Chapter 5

Integrals

5.1 | Areas and Distances | Exercises | p.266 |

5.2 | The Definite Integral | Exercises | p.279 |

5.3 | Evaluating Definite Integrals | Exercises | p.289 |

5.4 | The Fundamental Theorem of Calculus | Exercises | p.298 |

5.5 | The Substitution Rule | Exercises | p.306 |

Chapter 5 Review (True-False Quiz) | p.308 | ||

Chapter 5 Review (Concept Check) | p.308 | ||

Chapter 5 Review (Exercises) | p.309 |

### Chapter 6

Techniques Of Integration

6.1 | Integration by Parts | Exercises | p.316 |

6.2 | Trigonometric Integrals and Substitutions | Exercises | p.326 |

6.3 | Partial Fractions | Exercises | p.334 |

6.4 | Integration with Tables and Computer Algebra Systems | Exercises | p.340 |

6.5 | Approximate Integration | Exercises | p.350 |

6.6 | Improper Integrals | Exercises | p.360 |

Chapter 6 Review (Concept Check) | p.362 | ||

Chapter 6 Review (True-False Quiz) | p.362 | ||

Chapter 6 Review (Exercises) | p.363 |

### Chapter 7

Applications Of Integration

7.1 | Areas between Curves | Exercises | p.369 |

7.2 | Volumes | Exercises | p.378 |

7.3 | Volumes by Cylindrical Shells | Exercises | p.384 |

7.4 | Arc Length | Exercises | p.391 |

7.5 | Area of a Surface of Revolution | Exercises | p.397 |

7.6 | Applications to Physics and Engineering | Exercises | p.408 |

7.7 | Differential Equations | Exercises | p.418 |

Chapter 7 Review (Concept Check) | p.421 | ||

Chapter 7 Review (Exercises) | p.422 |

### Chapter 8

Series

8.1 | Sequences | Exercises | p.434 |

8.2 | Series | Exercises | p.443 |

8.3 | The Integral and Comparison Tests | Exercises | p.452 |

8.4 | Other Convergence Tests | Exercises | p.463 |

8.5 | Power Series | Exercises | p.468 |

8.6 | Representing Functions as Power Series | Exercises | p.474 |

8.7 | Taylor and Maclaurin Series | Exercises | p.487 |

8.8 | Applications of Taylor Polynomials | Exercises | p.494 |

Chapter 8 Review (Concept Check) | p.497 | ||

Chapter 8 Review (True-False Quiz) | p.497 | ||

Chapter 8 Review (Exercises) | p.498 |

### Chapter 9

Parametric Equations And Polar Coordinates

9.1 | Parametric Curves | Exercises | p.505 |

9.2 | Calculus with Parametric Curves | Exercises | p.513 |

9.3 | Polar Coordinates | Exercises | p.522 |

9.4 | Areas and Lengths in Polar Coordinates | Exercises | p.528 |

9.5 | Conic Sections in Polar Coordinates | Exercises | p.534 |

Chapter 9 Review (Concept Check) | p.535 | ||

Chapter 9 Review (Exercises) | p.535 | ||

Chapter 9 Review (True-False Quiz) | p.535 |

### Chapter 10

Vectors And The Geometry Of Space

10.1 | Three-Dimensional Coordinate Systems | Exercises | p.541 |

10.2 | Vectors | Exercises | p.549 |

10.3 | The Dot Product | Exercises | p.556 |

10.4 | The Cross Product | Exercises | p.564 |

10.5 | Equations of Lines and Planes | Exercises | p.572 |

10.6 | Cylinders and Quadric Surfaces | Exercises | p.579 |

10.7 | Vector Functions and Space Curves | Exercises | p.589 |

10.8 | Arc Length and Curvature | Exercises | p.598 |

10.9 | Motion in Space: Velocity and Acceleration | Exercises | p.608 |

Chapter 10 Review (Concept Check) | p.610 | ||

Chapter 10 Review (True-False Quiz) | p.611 | ||

Chapter 10 Review (Exercises) | p.612 |

### Chapter 11

Partial Derivatives

11.1 | Functions and Several Variables | Exercises | p.623 |

11.2 | Limits and Continuity | Exercises | p.632 |

11.3 | Partial Derivatives | Exercises | p.638 |

11.4 | Tangent Places and Linear Approximations | Exercises | p.648 |

11.5 | The Chain Rule | Exercises | p.656 |

11.6 | Directional Derivatives and the Gradient Vector | Exercises | p.667 |

11.7 | Maximum and Minimum Values | Exercises | p.675 |

11.8 | Lagrange Multipliers | Exercises | p.683 |

Chapter 11 Review (True-False Quiz) | p.685 | ||

Chapter 11 Review (Concept Check) | p.685 | ||

Chapter 11 Review (Exercises) | p.686 |

### Chapter 12

Multiple Integrals

12.1 | Double Integrals over Rectangles | Exercises | p.698 |

12.2 | Double Integrals over General Regions | Exercises | p.707 |

12.3 | Double Integrals in Polar Coordinates | Exercises | p.713 |

12.4 | Applications of Double Integrals | Exercises | p.720 |

12.5 | Triple Integrals | Exercises | p.728 |

12.6 | Triple Integrals in Cylindrical Coordinates | Exercises | p.734 |

12.7 | Triple Integrals in Spherical Coordinates | Exercises | p.740 |

12.8 | Change of Variables in Multiple Integrals | Exercises | p.749 |

Chapter 12 Review (True-False Quiz) | p.751 | ||

Chapter 12 Review (Concept Check) | p.751 | ||

Chapter 12 Review (Exercises) | p.752 |

### Chapter 13

Vector Calculus

13.1 | Vector Fields | Exercises | p.760 |

13.2 | Line Integral | Exercises | p.770 |

13.3 | The Fundamental Theorem for Line Integrals | Exercises | p.780 |

13.4 | Green's Theorem | Exercises | p.787 |

13.5 | Curl and Divergence | Exercises | p.795 |

13.6 | Parametric Surfaces and Their Areas | Exercises | p.805 |

13.7 | Surface Integrals | Exercises | p.816 |

13.8 | Stoke's Theorem | Exercises | p.822 |

13.9 | The Divergence Theorem | Exercises | p.829 |

Chapter 13 Review (Concept Check) | p.830 | ||

Chapter 13 Review (True-False Quiz) | p.831 | ||

Chapter 13 Review (Exercises) | p.831 |