Chapter 1. Limits and Continuity
1. Introduction to Limits | 10
2. Trigonometric and Infinite Limits | 20
3. Continuity | 33
4. Chapter Test | 42
Chapter 2. Differentiation
1. Definition of Derivatives | 50
2. Basic Differentiation Rules, Part 1 | 59
3. Basic Differentiation Rules, Part 2 | 72
4. Implicit Differentiation | 82
5. Derivatives of Inverse Functions | 88
6. Chapter Test | 95
Chapter 3. Applications of Differentiation, Part 1
1. Tangent and Normal Lines and Linear Approximation | 106
2. The Mean Value Theorem and Rolle¡¯s Theorem | 112
3. Extrema and the First Derivative Test | 118
4. Concavity and the Second Derivative Test | 126
5. Graphs of f, f', and f " | 136
6. Chapter Test | 144
Chapter 4. Applications of Differentiation, Part 2
1. Motion along a Line | 154
2. Related Rates | 162
3. Optimization | 172
4. More Applications of Differentiation | 180
5. Chapter Test | 186
Chapter 5. Integration and its Techniques
...1. Introduction to Indefinite Integration | 196
2. Riemann Sums and Definite Integrals | 202
3. The Fundamental Theorem of Calculus | 216
4. Integration by Substitution | 232
5. Integration by Parts BC ONLY | 238
6. Integration by Linear Partial Fractions BC ONLY | 244
7. Improper Integrals BC ONLY | 247
8. Chapter Test | 253
Chapter 6. Application of Integration
1. Area of a Region | 272
2. Volume of Solids | 278
3. Arc Length BC ONLY | 291
4. Parametric Equations and Calculus BC ONLY | 295
5. Motions and Vectors | 301
6. Polar Equations and Calculus BC ONLY | 311
7. Chapter Test | 323
Chapter 7. Differential Equations
1. Separable Differential Equations | 338
2. Slope Fields and Euler¡¯s Method | 344
3. The Logistic Differential Equations BC ONLY | 352
4. Chapter Test | 358
Chapter 8. Infinite Series BC ONLY
1. Test for Convergence, Part 1 | 362
2. Test for Convergence, Part 2 | 368
3. Test for Convergence, Part 3 | 375
4. Taylor Polynomials and Approximations | 393
5. Power Series | 408
6. Chapter Test | 415
Solutions Manual