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Preface | |
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Functions | |
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Introduction | |
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The Graph of a Function | |
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The Trigonometric Functions | |
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Inverse Functions and the Inverse Trigonometric Functions | |
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Exponential and Logarithm Functions | |
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Solving Inequalities Involving Elementary Functions | |
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Graphs of Translations, Reflections, Expansions and Sums | |
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Review of Problems for Chapter 1 | |
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Limits | |
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Introduction | |
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Finding Limits of Combinations of Functions | |
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Indeterminate Limits | |
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Review Problems for Chapter 2 | |
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The Derivative Part I: Preview | |
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Definition and Some Applications of the Derivative | |
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Derivatives of the Basic Functions | |
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Nondifferentiable Functions | |
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Derivatives of Constant Multiples, Sums, Products and Quotients | |
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The Derivative of a Composition | |
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Implicit Differentiation and Logarithmic Differentiation | |
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Antidifferentiation | |
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Review Problems for Chapter 3 | |
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The Derivative Part II: Relative Maxima and Minima | |
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Absolute Maxima and Minima | |
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L'H(pital's Rule and Orders of Magnitude | |
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Indeterminate Products, Differences and Exponential Forms | |
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Drawing Graphs of Functions | |
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Related Rates | |
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Newton's Method | |
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Differentials | |
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Separable Differential Equations | |
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Review Problems for Chapter 4 | |
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The Integral Part I: Preview | |
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Definition and Some Applications of the Integral | |
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The Fundamental Theorem of Calculus | |
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Numerical Integration | |
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Nonintegrable Functions | |
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Improper Integals | |
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Review Problems for Chapter 5 | |
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The Integral Part II: Further Applications of the Integral | |
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The Centroid of a Solid Hemisphere | |
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Area and Arc Length | |
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The Surface Area of a Cone and a Sphere | |
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Integrals with a Variable Upper Limit | |
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Review Problems for Chapter 6 | |
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Antidifferentiation | |
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Introduction | |
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Substitution | |
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Pre-Table Algebra I | |
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Pre-Table Algebra II: Partial Faction Decomposition | |
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Integration by Parts | |
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Recursion Formulas | |
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Trigonometric Substitution | |
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Choosing a Method | |
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Combining Techniques of Antidifferentiation with the Fundamental Theorem | |
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Review Problems for Chapter 7 | |
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Series | |
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Introduction | |
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Geometric Series | |
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Convergence Tests for Positive Series I | |
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Convergence Tests for Positive Series II | |
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Alternating Series | |
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Power Series Functions | |
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Power Series Representations for Elementary Functions I | |
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Power Series Representations for Elementary Functions II (Maclaurin Series) | |
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The Taylor Reminder Formula and an Estimate for the Number e | |
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Power Series in Powers of x - b (Taylor Series) | |
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Review Problems for Chapter 8 | |
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Vectors | |
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Introduction | |
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Vector Addition, Subtraction, Scalar Multiplication and Norms | |
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The Dot Product | |
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The Cross Product | |
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The Scalar Triple Product | |
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The Velocity Vector | |
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The Acceleration Vector | |
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Review Problems for Chapter 9 | |
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Topics in Three-Dimensional Analytic Geometry | |
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Spheres | |
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Planes | |
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Lines | |
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Cylindrical and Quadric Surfaces | |
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Cylindrical and Spherical Coordinates | |
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Review Problems for Chapter 10 | |
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Partial Derivatives | |
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Graphs and Level Sets | |
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Partial Derivatives | |
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Chain Rules for First-Order Partial Derivatives | |
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Chain Rules for Second-Order Partial Derivatives | |
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Maxima and Minima | |
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The Gradient | |
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Dif | |