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Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises | |
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Preface A User's Guide to Features Integrating Excel Graphing Calculator Terminology | |
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Functions | |
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Real Numbers, Inequalities, and Lines | |
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Exponents | |
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Functions | |
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Functions, Continued | |
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Derivatives and Their Uses | |
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Limits and Continuity | |
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Rates of Change, Slopes, and Derivatives | |
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Some Differentiation Formulas | |
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The Product and Quotient Rules | |
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HigherOrder Derivatives | |
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The Chain Rule and the Generalized Power Rule | |
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Nondifferentiable Functions | |
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Further Applications of Derivatives | |
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Graphing Using the First Derivative | |
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Graphing Using the First and Second Derivatives | |
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Optimization | |
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Further Applications of Optimization | |
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Optimizing Lot Size and Harvest Size | |
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Implicit Differentiation and Related Rates | |
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Cumulative Review for Chapters 13 | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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Logarithmic Functions | |
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Differentiation of Logarithmic and Exponential Functions | |
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Two Applications to Economics: Relative Rates and Elasticity of Demand | |
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Integration and Its Applications | |
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Antiderivatives and Indefinite Integrals | |
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Integration Using Logarithmic and Exponential Functions | |
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Definite Integrals and Areas | |
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Further Applications of Definite Integrals: Average Value and Area Between Curves | |
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Two Applications to Economics: Consumers' Surplus and Income Distribution | |
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Integration by Substitution | |
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Integration Techniques | |
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Integration by Parts | |
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Integration Using Tables | |
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Improper Integrals | |
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Numerical Integration | |
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Calculus of Several Variables | |
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Functions of Several Variables | |
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Partial Derivatives | |
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Optimizing Functions of Several Variables | |
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Least Squares | |
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Lagrange Multipliers and Constrained Optimization | |
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Total Differentials and Approximate Changes | |
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Multiple Integrals | |
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Cumulative Review for Chapters 17 | |
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Trigonometric Functions | |
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Triangles, Angles, and Radian Measure | |
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Sine and Cosine Functions | |
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Derivatives of Sine and Cosine Functions | |
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Integrals of Sine and Cosine Functions | |
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Other Trigonometric Functions | |
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Differential Equations | |
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Separation of Variables | |
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Further Applications of Differential Equations: Three Models of Growth | |
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FirstOrder Linear Differential Equations | |
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Approximate Solutions of Differential Equations: Euler's Method | |
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Sequences and Series | |
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Geometric Series | |
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Taylor Polynomials | |
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Taylor Series | |
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Newton's Method | |
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Probability | |
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Discrete Probability | |
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Continuous Probability | |
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Uniform and Exponential Random Variables | |
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Normal Random Variables | |
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Cumulative Review for Chapters 111 | |
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Appendix | |
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Answers to Selected Exercises | |
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Index | |