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| About the Authors | |
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| Preface | |
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| Functions, Graphs, and Models | |
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| Functions and Mathematical ModelingInvestigation: Designing a Wading Pool | |
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| Graphs of Equations and Functions | |
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| Polynomials and Algebraic Functions | |
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| Transcendental Functions | |
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| Preview: What Is Calculus? | |
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| Review - Understanding: Concepts and Definitions | |
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| Objectives: Methods and Techniques | |
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| Prelude to Calculus | |
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| Tangent Lines and Slope Predictors | |
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| Investigation: Numerical Slope Investigations | |
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| The Limit ConceptInvestigation: Limits, Slopes, and Logarithms | |
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| More About LimitsInvestigation: Numerical Epsilon-Delta Limits | |
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| The Concept of Continuity | |
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| Review - Understanding: Concepts and Definitions | |
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| Objectives: Methods and Techniques | |
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| The Derivative | |
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| The Derivative and Rates of Change | |
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| Basic Differentiation Rules | |
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| The Chain Rule | |
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| Derivatives of Algebraic Functions | |
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| Maxima and Minima of Functions on Closed Intervals | |
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| Investigation: When Is Your Coffee Cup Stablest? | |
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| Applied Optimization Problems | |
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| Derivatives of Trigonometric Functions | |
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| Exponential and Logarithmic Functions | |
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| Investigation: Discovering the Number e for Yourself | |
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| Implicit Differentiation and Related Rates | |
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| Investigation: Constructing the Folium of Descartes | |
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| Successive Approximations and Newton's Method | |
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| Investigation: How Deep Does a Floating Ball Sink? | |
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| Review - Understanding: Concepts, Definitions, and Formulas | |
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| Objectives: Methods and Techniques | |
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| Additional Applications of the Derivative | |
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| Introduction | |
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| Increments, Differentials, and Linear Approximation | |
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| Increasing and Decreasing Functions and the Mean Value Theorem | |
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| The First Derivative Test and Applications | |
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| Investigation: Constructing a Candy Box With Lid | |
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| Simple Curve Sketching | |
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| Higher Derivatives and Concavity | |
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| Curve Sketching and Asymptotes | |
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| Investigation: Locating Special Points on Exotic Graphs | |
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| Indeterminate Forms and L'Hapital's Rule | |
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| More Indeterminate Forms | |
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| Review - Understanding: Concepts, Definitions, and Results | |
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| Objectives: Methods and Techniques | |
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| The Integral | |
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| Introduction | |
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| Antiderivatives and Initial Value Problems | |
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| Elementary Area Computations | |
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| Riemann Sums and the Integral | |
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| Investigation: Calculator/Computer Riemann Sums | |
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| Evaluation of Integrals | |
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| The Fundamental Theorem of Calculus | |
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| Integration by Substitution | |
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| Areas of Plane Regions | |
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| Numerical IntegrationInvestigation: Trapezoidal and Simpson Approximations | |
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| Review - Understanding: Concepts, Definitions, and Results | |
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| Objectives: Methods and Techniques | |
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| Applications of the Integral | |
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| Riemann Sum Approximations | |
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| Volumes by the Method of Cross Sections | |
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| Volumes by the Method of Cylindrical Shells | |
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| Investigation: Design Your Own Ring! | |
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| Arc Length and Surface Area of Revolution | |
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| Force and Work | |
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| Centroids of Plane Regions and Curves | |
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| The Natural Logarithm as an Integral | |
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| Investigation: Natural Functional Equations | |
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| Inverse Trigonometric Functions | |
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| Hyperbolic Functions | |
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| Review - Understanding: Concepts, Definitions, and Formulas | |
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| Objectives: Methods and Techniques | |
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| Techniques of Integration | |
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| Introduction< | |