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| (NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.) | |
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| P. Preliminaries | |
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| Real Numbers and the Real Line | |
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| Coordinates, Lines, and Increments | |
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| Functions | |
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| Shifting Graphs | |
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| Trigonometric Functions | |
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| Limits and Continuity | |
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| Rates of Change and Limits | |
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| Rules for Finding Limits | |
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| Target Values and Formal Definitions of Limits | |
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| Extensions of the Limit Concept | |
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| Continuity | |
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| Tangent Lines | |
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| Derivatives | |
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| The Derivative of a Function | |
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| Differentiation Rules | |
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| Rates of Change | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Implicit Differentiation and Rational Exponents | |
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| Related Rates of Change | |
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| Applications of Derivatives | |
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| Extreme Values of Functions | |
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| The Mean Value Theorem | |
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| The First Derivative Test for Local Extreme Values | |
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| Graphing with y e and y deg | |
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| Limits as x aelig; a, Asymptotes, and Dominant Terms | |
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| Optimization Linearization and Differentials | |
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| Newton's Method | |
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| Integration | |
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| Indefinite Integrals | |
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| Differential Equations, Initial Value Problems, and Mathematical Modeling | |
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| Integration by Substitution-Running the Chain Rule Backward | |
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| Estimating with Finite Sums | |
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| Riemann Sums and Definite Integrals | |
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| Properties, Area, and the Mean Value Theorem | |
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| Substitution in Definite Integrals | |
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| Numerical Integration | |
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| Applications of Integrals | |
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| Areas Between Curves | |
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| Finding Volumes by Slicing | |
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| Volumes of Solids of Revolution-Disks and Washers | |
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| Cylindrical Shells Lengths of Plan Curves | |
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| Areas of Surfaces of Revolution | |
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| Moments and Centers of Mass | |
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| Work | |
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| Fluid Pressures and Forces | |
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| The Basic Pattern and Other Modeling Applications | |
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| Transcendental Functions | |
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| Inverse Functions and Their Derivatives | |
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| Natural Logarithms | |
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| The Exponential Function | |
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| ax and logax | |
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| Growth and Decay | |
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| L'Hocirc;pital's Rule | |
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| Relative Rates of Growth | |
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| Inverse Trigonomic Functions | |
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| Derivatives of Inverse Trigonometric Functions; Integrals | |
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| Hyperbolic Functions | |
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| First Order Differential Equations | |
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| Euler's Numerical Method; Slope Fields | |
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| Techniques of Integration | |
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| Basic Integration Formulas | |
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| Integration by Parts | |
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| Partial Fractions | |
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| Trigonometric Substitutions | |
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| Integral Tables and CAS | |
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| Improper Integrals | |
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| Infinite Series | |
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| Limits of Sequences of Numbers | |
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| Theorems for Calculating Limits of Sequences | |
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| Infinite Series | |
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| The Integral Test for Series of Nonnegative Terms | |
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| Comparison Tests for Series of Nonnegative Terms | |
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| The Ratio and Root Tests for Series of Nonnegative Terms | |
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| Alternating Series, Absolute and Conditional Convergence | |
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| Power Series | |
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| Taylor and Maclaurin Series | |
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| Convergence of Taylor Series; Error Estimates | |
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| Applications of Power Series | |
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| Conic Sections, Parametrized Curves, and Polar Coordinates | |
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| Conic Sections and Quadratic Equations | |
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| Classifying Conic Sections by Eccentricity | |
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| Quadratic Equations and Rotations | |
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| Parametrizations of Plan Curves | |
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| Calculus with Parametrized Curves | |
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| Polar Coordinates | |
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| Graphing in Polar Coordinates | |
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| Polar Equations for Conic Sections | |
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| Integration in Polar Coordinates | |
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| Vectors and Analytic Geometry in Space | |
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| Vectors in the Plane | |
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| Cartesian (Rectangular) Coordinates and Vectors in Space | |
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| Dot Products | |
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| Cross Products | |
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| Lines and Planes in Space | |
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| Cylinders and Quadric Surfaces | |
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| Cylindrical and Spherical Coordinates | |
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| Vector-Valued Functions and Motion in Space | |
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| Vector-Valued Functions and Space Curves | |
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| Modeling Projectile Motion | |
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| Arc Length and the Unit Tangent Vector T | |
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| Curvature, Torison, and the TNB Frame | |