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Functions and Models | |
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Four Ways to Represent a Function | |
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Mathematical Models: A Catalog of Essential Functions | |
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New Functions from Old Functions | |
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Graphing Calculators and Computers | |
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Exponential Functions | |
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Inverse Functions and Logarithms | |
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Review | |
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Principles of Problem Solving | |
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Limits and Derivatives | |
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The Tangent and Velocity Problems | |
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The Limit of a Function | |
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Calculating Limits Using the Limit Laws | |
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The Precise Definition of a Limit | |
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Continuity | |
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Limits at Infinity | |
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Horizontal Asymptotes | |
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Derivatives and Rates of Change | |
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Writing Project: Early Methods for Finding Tangents | |
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The Derivative as a Function | |
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Review | |
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Problems Plus | |
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Differentiation Rules | |
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Derivatives of Polynomials and Exponential Functions | |
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Applied Project: Building a Better Roller Coaster | |
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The Product and Quotient Rules | |
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Derivatives of Trigonometric Functions | |
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The Chain Rule | |
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Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation | |
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Derivatives of Logarithmic Functions | |
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Rates of Change in the Natural and Social Sciences | |
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Exponential Growth and Decay | |
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Related Rates | |
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Linear Approximations and Differentials | |
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Laboratory Project: Taylor Polynomials | |
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Hyperbolic Functions | |
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Review | |
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Problems Plus | |
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Applications of Differentiation | |
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Maximum and Minimum Values | |
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Applied Project: The Calculus of Rainbows | |
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The Mean Value Theorem | |
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How Derivatives Affect the Shape of a Graph | |
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Indeterminate Forms and L'Hospital's Rule | |
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Writing Project: The Origins of L'Hospital's Rule | |
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Summary of Curve Sketching | |
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Graphing with Calculus and Calculators | |
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Optimization Problems | |
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Applied Project: The Shape of a Can | |
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Applications to Business and Economics | |
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Newton's Method | |
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Antiderivatives | |
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Review | |
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Problems Plus | |
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Integrals | |
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Areas and Distances | |
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The Definite Integral | |
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Discovery Project: Area Functions | |
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The Fundamental Theorem of Calculus | |
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Indefinite Integrals and the Total Change Theorem | |
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Writing Project: Newton, Leibniz, and the Invention of Calculus | |
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The Substitution Rule | |
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Review | |
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Problems Plus | |
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Applications of Integration | |
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Areas between Curves | |
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Volume | |
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Volumes by Cylindrical Shells | |
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Work | |
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Average Value of a Function | |
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Applied Project: Where to Sit at the Movies | |
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Review | |
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Problems Plus | |
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Appendixes | |
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Intervals, Inequalities, and Absolute Values | |
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Coordinate Geometry and Lines | |
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Graphs of Second-Degree Equations | |
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Trigonometry | |
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Sigma Notation | |
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Proofs of Theorems | |
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Complex Numbers | |
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Answers to Odd-Numbered Exercises | |