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| 1.1: | Four Ways to Represent a Function |
| 1.2: | Mathematical Models: A Catalog of Essential Functions |
| 1.3: | New Functions from Old Functions |
| 2.1: | The Tangent and Velocity Problems |
| 2.2: | The Limit of a Function |
| 2.3: | Calculating Limits Using the Limit Laws |
| 2.4: | The Precise Definition of a Limit |
| 2.5: | Continuity |
| 3.1: | Derivatives and Rates of Change |
| 3.2: | The Derivative as a Function |
| 3.3: | Differentiation Formulas |
| 3.4: | Derivatives of Trigonometric Functions |
| 3.5: | The Chain Rule |
| 3.6: | Implicit Differentiation |
| 3.7: | Rates of Change in the Natural and Social Sciences |
| 3.9: | Linear Approximations and Differentials |
| 4.1: | Maximum and Minimum Values |
| 4.2: | The Mean Value Theorem |
| 4.3: | How Derivatives Affect the Shape of a Graph |
| 4.4: | Limits at Infinity: Horizontal Asymptotes |
| 4.5: | Summary of Curve Sketching |
| 4.7: | Optimization Problems |
| 4.8: | Newton's Method |
| 4.9: | Antiderivatives |
| 5.1: | Areas and Distances |
| 5.2: | The Definite Integral |
| 5.3: | The Fundamental Theorem of Calculus |
| 5.4: | Indefinite Integrals and the Net Change Theorem |
| 5.5: | The Substitution Rule |
| 6.1: | Areas Between Curves |
| 6.2: | Volumes |
| 6.3: | Volumes by Cylindrical Shells |
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