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