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Test Yourself Chapter 1 Functions 1.1 Functions and Graphs 1.2 Combining Functions 1.3 Polynomial and Rational Functions 1.4 Transcendental Functions 1.5 Inverse Functions 1.6 Exponential and Logarithmic Functions 1.7 From Words to Functions Chapter 1 in Review Chapter 2 Limit of a Function 2.1 Limits ¿ An Informal Approach 2.2 Limit Theorems 2.3 Continuity 2.4 Trigonometric Limits 2.5 Limits that Involve Infinity 2.6 Limits ¿ A Formal Approach 2.7 The Tangent Line Problem Chapter 2 in Review Chapter 3 The Derivative 3.1 The Derivative 3.2 Power and Sum Rules 3.3 Product and Quotient Rules 3.4 Trigonometric Functions 3.5 Chain Rule 3.6 Implicit Differentiation 3.7 Derivatives of Inverse Functions 3.8 Exponential Functions 3.9 Logarithmic Functions 3.10 Hyperbolic Functions Chapter 3 in Review Chapter 4 Applications of the Derivative 4.1 Rectilinear Motion 4.2 Related Rates 4.3 Extrema of Function 4.4 Mean Value Theorem 4.5 Limits Revisited - L¿Hôpital¿s Rule 4.6 Graphing and the First Derivative 4.7 Graphing and the Second Derivative 4.8 Optimization 4.9 Linearization and Differentials 4.10 Newton¿s Method Chapter 4 in Review Chapter 5 Integrals 5.1 The Indefinite Integral 5.2 Integration by the u-Substitution 5.3 The Area Problem 5.4 The Definite Integral 5.5 Fundamental Theorem of Calculus Chapter 5 in Review Chapter 6 Applications of the Integral 6.1 Rectilinear Motion Revisited 6.2 Area Revisited 6.3 Volumes of Solids: Slicing Method 6.4 Volumes of Solids: Shell Method 6.5 Length of a Graph 6.6 Area of a Surface of Revolution 6.7 Average Value of a Function 6.8 Work 6.9 Liquid Pressure and Force 6.10 Centers of Mass and Centroids Chapter 6 in Review Chapter 7 Techniques of Integration 7.1 Integration ¿ Three Resources 7.2 Integration by Substitution 7.3 Integration by Parts 7.4 Powers of Trigonometric Functions 7.5 Trigonometric Substitutions 7.6 Partial Fractions 7.7 Improper Integrals 7.8 Approximate Integration Chapter 7 in Review Chapter 8 First-Order Differential Equations 8.1 Separable Equations 8.2 Linear Equations 8.3 Mathematical Models 8.4 Solution Curves without a Solution 8.4 Euler¿s Method Chapter 8 in Review Chapter 9 Sequences and Series 9.1 Sequences 9.2 Monotonic Sequences 9.3 Series 9.4 Integral Test 9.5 Comparison Tests 9.6 Ratio and Root Tests 9.7 Alternating Series 9.8 Power Series 9.9 Representing Functions by Power Series 9.10 Taylor Series 9.11 Binomial Series Chapter 9 in Review Chapter 10 Conics and Polar Coordinates 10.1 Conic Sections 10.2 Parametric Equations 10.3 Calculus and Parametric Equations 10.5 Polar Coordinate System 10.5 Graphs of Polar Equations 10.6 Calculus in Polar Coordinates 10.7 Conic Sections in Polar Coordinates Chapter 10 in Review Appendix Proofs of Selected Theorems Answers to Test Yourself Answers to Selected Odd-Numbered Problems Resource Pages Review of Algebra Formulas from Geometry Graphs and Functions Review of Trigonometry Exponential and Logarithmic Functions Differentiation Integration Formulas

Library of Congress Subject Headings for this publication:

Calculus.