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| Preparation for Calculus | |
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| Graphs and Models | |
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| Linear Models and Rates of Change | |
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| Functions and Their Graphs | |
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| Fitting Models to Data | |
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| Limits and Their Properties | |
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| A Preview of Calculus | |
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| Finding Limits Graphically and Numerically | |
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| Evaluating Limits Analytically | |
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| Continuity and One-Sided Limits | |
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| Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions | |
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| Differentiation | |
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| The Derivative and the Tangent Line Problem | |
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| Basic Differentiation Rules and Rates of Change | |
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| Product and Quotient Rules and Higher-Order Derivatives | |
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| The Chain Rule | |
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| Implicit Differentiation Section Project: Optical Illusions | |
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| Related Rates | |
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| Applications of Differentiation | |
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| Extrema on an Interval | |
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| Rolle\'s Theorem and the Mean Value Theorem | |
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| Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |
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| Concavity and the Second Derivative Test | |
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| Limits at Infinity | |
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| A Summary of Curve Sketching | |
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| Optimization Problems Section Project: Connecticut River | |
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| Newton\'s Method | |
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| Differentials | |
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| Integration | |
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| Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals | |
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| The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |
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| Integration by Substitution | |
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| Numerical Integration | |
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| Logarithmic, Exponential, and Other Transcendental Functions | |
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| The Natural Logarithmic Function: Differentiation | |
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| The Natural Logarithmic Function: Integration | |
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| Inverse Functions | |
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| Exponential Functions: Differentiation and Integration | |
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| Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |
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| Inverse Trigonometric Functions: Differentiation | |
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| Inverse Trigonometric Functions: Integration | |
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| Hyperbolic Functions Section Project: St. Louis Arch | |
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| Differential Equations | |
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| Slope Fields and Euler\'s Method | |
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| Differential Equations: Growth and Decay | |
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| Separation of Variables and the Logistic Equation | |
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| First-Order Linear Differential Equations Section Project: Weight Loss | |
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| Applications of Integration | |
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| Area of a Region Between Two Curves | |
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| Volume: The Disk Method | |
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| Volume: The Shell Method Section Project: Saturn | |
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| Arc Length and Surfaces of Revolution | |
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| Work Section Project: Tidal Energy | |
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| Moments, Centers of Mass, and Centroids | |
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| Fluid Pressure and Fluid Force | |
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| Integration Techniques, L\'H?pital\'s Rule, and Improper Integrals | |
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| Basic Integration Rules | |
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| Integration by Parts | |
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| Trigonometric Integrals Section Project: Power Lines | |
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| Trigonometric Substitution | |
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| Partial Fractions | |
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| Integration by Tables and Other Integration Techniques | |
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| Indeterminate Forms and L\'H?pital\'s Rule 8.8 Improper Integrals | |
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| Infinite Series | |
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| Sequences | |
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| Series and Convergence Section Project: Cantor\'s Disappearing Table | |
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| The Integral Test and p-Series Section Project: The Harmonic Series | |
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| C | |