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Preliminaries | |
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Lines | |
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Functions and Their Graphs | |
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The Trigonometric Functions | |
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Combining Functions | |
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Graphing Calculators and Computers | |
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Mathematical Models | |
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Chapter Review | |
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Limits | |
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An Intuitive Introduction to Limits | |
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Techniques for Finding Limits | |
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A Precise Definition of a Limit | |
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Continuous Functions | |
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Tangent Lines and Rates of Change | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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The Derivative | |
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The Derivative | |
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Basic Rules of Differentiation | |
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The Product and Quotient Rules | |
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The Role of the Derivative in the Real World | |
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Derivatives of Trigonometric Functions | |
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The Chain Rule | |
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Implicit Differentiation | |
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Related Rates | |
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Differentials and Linear Approximations | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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Applications Of The Derivative | |
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Extrema of Functions | |
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The Mean Value Theorem | |
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Increasing and Decreasing Functions and the FirSt. Derivative TeSt. Concavity and Inflection Points | |
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Limits Involving Infinity | |
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Asymptotes | |
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Curve Sketching | |
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Optimization Problems | |
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Newton's Method | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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Integration | |
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Indefinite Integrals | |
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Integration by Substitution | |
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Area | |
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The Definite Integral | |
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The Fundamental Theorem of Calculus | |
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Numerical Integration | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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Applications Of The Definite Integral | |
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Areas Between Curves | |
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Volumes: Disks, Washers, and Cross Sections | |
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Volumes Using Cylindrical Shells | |
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Arc Length and Areas of Surfaces of Revolution | |
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Work | |
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Fluid Pressure and Force | |
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Moments and Centers of Mass | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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The Transcendental Functions | |
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The Natural Logarithmic Function | |
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Inverse Functions | |
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Exponential Functions | |
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General Exponential and Logarithmic Functions | |
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Inverse Trigonometric Functions | |
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Hyperbolic Functions | |
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Indeterminate Forms and L'H?pital's Rule | |
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Chapter Review | |
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Challenge Problems | |
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Techniques Of Integration | |
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Integration by Parts | |
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Trigonometric Integrals | |
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Trigonometric Substitutions | |
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The Method of Partial Fractions | |
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Integration Using Tables of Integrals and CAS | |
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Improper Integrals | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |
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Differential Equations | |
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Differential Equations: Separable Equations | |
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Direction Fields and Euler's Method | |
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The Logistic Equation | |
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First-Order Linear Differential Equations | |
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Chapter Review | |
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Challenge Problems | |
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Infinite Sequences And Series | |
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Sequences | |
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Series | |
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The Integral TeSt. The Comparison Tests | |
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Alternating Series | |
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Absolute Convergence | |
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The Ratio and Root Tests | |
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Power Series | |
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Taylor and Maclaurin Series | |
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Approximation by Taylor Polynomials | |
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Chapter Review | |
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Problem-Solving Techniques | |
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Challenge Problems | |