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| Preface | |
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| Introduction | |
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| Functions | |
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| Functions and Their Graphs | |
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| Some Important Functions | |
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| The Algebra of Functions | |
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| Zeros of Functions-The Quadratic Formula and Factoring | |
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| Exponents and Power Functions | |
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| Functions and Graphs in Applications | |
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| The Derivative | |
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| The Slope of a Straight Line | |
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| The Slope of a Curve at a Point | |
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| The Derivative | |
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| Limits and the Derivative | |
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| Differentiability and Continuity | |
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| Some Rules for Differentiation | |
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| More About Derivatives | |
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| The Derivative as a Rate of Change | |
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| Applications of the Derivative | |
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| Describing Graphs of Functions | |
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| The First and Second Derivative Rules | |
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| The First and Second Derivative Tests and Curve Sketching | |
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| Curve Sketching (Conclusion) | |
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| Optimization Problems | |
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| Further Optimization Problems | |
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| Applications of Derivatives to Business and Economics | |
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| Techniques of Differentiation | |
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| The Product and Quotient Rules | |
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| The Chain Rule and the General Power Rule | |
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| Implicit Differentiation and Related Rates | |
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| Logarithm Functions | |
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| Exponential Functions | |
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| The Exponential Function ex | |
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| Differentiation of Exponential Functions | |
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| The Natural Logarithm Function | |
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| The Derivative of ln x | |
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| Properties of the Natural Logarithm Function | |
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| Applications of the Exponential and Natural Logarithm Functions | |
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| Exponential Growth and Decay | |
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| Compound Interest | |
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| Applications of the Natural Logarithm Function to Economics | |
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| Further Exponential Models | |
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| The Definite Integral | |
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| Antidifferentiation | |
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| Areas and Riemann Sums | |
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| Definite Integrals and the Fundamental Theorem | |
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| Areas in the xy-Plane | |
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| Applications of the Definite Integral | |
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| Functions of Several Variables | |
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| Examples of Functions of Several Variables | |
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| Partial Derivatives | |
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| Maxima and Minima of Functions of Several Variables | |
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| Lagrange Multipliers and Constrained Optimization | |
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| The Method of Least Squares | |
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| Double Integrals | |
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| The Trigonometric Functions | |
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| Radian Measure of Angles | |
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| The Sine and the Cosine | |
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| Differentiation and Integration of sin t and cos t | |
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| The Tangent and Other Trigonometric Functions | |
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| Techniques of Integration | |
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| Integration by Substitution | |