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Table of Contents

Orientation Quizzes.- R Review of Fundamentals.- R.1 Basic Algebra: Real Numbers and Inequalities.- R.2 Intervals and Absolute Values.- R.3 Laws of Exponents.- R.4 Straight Lines.- R.5 Circles and Parabolas.- R.6 Functions and Graphs.- 1 Derivatives and Limits.- 1.1 Introduction to the Derivative.- 1.2 Limits.- 1.3 The Derivative as a Limit and the Leibniz Notation.- 1.4 Differentiating Polynomials.- 1.5 Products and Quotients.- 1.6 The Linear Approximation and Tangent Lines.- 2 Rates of Change and the Chain Rule.- 2.1 Rates of Change and the Second Derivative.- 2.2 The Chain Rule.- 2.3 Fractional Powers and Implicit Differentiation.- 2.4 Related Rates and Parametric Curves.- 2.5 Antiderivatives.- 3 Graphing and Maximum—Minimum Problems.- 3.1 Continuity and the Intermediate Value Theorem.- 3.2 Increasing and Decreasing Functions.- 3.3 The Second Derivative and Concavity.- 3.4 Drawing Graphs.- 3.5 Maximum—Minimum Problems.- 3.6 The Mean Value Theorem.- 4 The Integral.- 4.1 Summation.- 4.2 Sums and Areas.- 4.3 The Definition of the Integral.- 4.4 The Fundamental Theorem of Calculus.- 4.5 Definite and Indefinite Integrals.- 4.6 Applications of the Integral.- 5 Trigonometric Functions.- 5.1 Polar Coordinates and Trigonometry.- 5.2 Differentiation of the Trigonometric Functions.- 5.3 Inverse Functions.- 5.4 The Inverse Trigonometric Functions.- 5.5 Graphing and Word Problems.- 5.6 Graphing in Polar Coordinates.- 6 Exponentials and Logarithms.- 6.1 Exponential Functions.- 6.2 Logarithms.- 6.3 Differentiation of the Exponential and Logarithmic Functions.- 6.4 Graphing and Word Problems.- Answers A.1.- Index I.1.