Introduction 1 What You''ll Find 1 Beyond the Book 2 Where to Go for Additional Help 2 Part 1: The Questions 5 Chapter 1: Algebra Review 7 The Problems You''ll Work On 7 What to Watch Out For 7 Simplifying Fractions 8 Simplifying Radicals 8 Writing Exponents Using Radical Notation 9 The Horizontal Line Test 9 Find Inverses Algebraically 10 The Domain and Range of a Function and Its Inverse 10 Linear Equations 10 Quadratic Equations 11 Solving Polynomial Equations by Factoring 11 Absolute Value Equations 12 Solving Rational Equations 12 Polynomial and Rational Inequalities 12 Absolute Value Inequalities 13 Graphing Common Functions 13 Domain and Range from a Graph 14 End Behavior of Polynomials 15 Adding Polynomials 15 Subtracting Polynomials 15 Multiplying Polynomials 16 Long Division of Polynomials 16 Chapter 2: Trigonometry Review 17 The Problems You''ll Work On 17 What to Watch Out For 17 Basic Trigonometry 18 Converting Degree Measure to Radian Measure 18 Converting Radian Measure to Degree Measure 19 Finding Angles in the Coordinate Plane 19 Finding Common Trigonometric Values 21 Simplifying Trigonometric Expressions 21 Solving Trigonometric Equations 22 Amplitude, Period, Phase Shift, and Midline 23 Equations of Periodic Functions 24 Inverse Trigonometric Function Basics 26 Solving Trigonometric Equations Using Inverses 27 Chapter 3: Limits and Rates of Change 29 The Problems You''ll Work On 29 What to Watch Out For 29 Finding Limits from Graphs 30 Evaluating Limits 31 Applying the Squeeze Theorem 32 Evaluating Trigonometric Limits 33 Infinite Limits 33 Limits from Graphs 36 Limits at Infinity 37 Horizontal Asymptotes 38 Classifying Discontinuities 38 Continuity and Discontinuities 39 Making a Function Continuous 40 The Intermediate Value Theorem 41 Chapter 4: Derivative Basics 43 The Problems You''ll Work On 43 What to Watch Out For 43 Determining Differentiability from a Graph 44 Finding the Derivative by Using the Definition 45 Finding the Value of the Derivative Using a Graph 46 Using the Power Rule to Find Derivatives 47 Finding All Points on a Graph Where Tangent Lines Have a Given Value 48 Chapter 5: The Product, Quotient, and Chain Rules 49 The Problems You''ll Work On 49 What to Watch Out For 49 Using the Product Rule to Find Derivatives 50 Using the Quotient Rule to Find Derivatives 51 Using the Chain Rule to Find Derivatives 53 More Challenging Chain Rule Problems 54 Chapter 6: Exponential and Logarithmic Functions and Tangent Lines 55 The Problems You''ll Work On 55 What to Watch Out For 55 Derivatives Involving Logarithmic Functions 56 Logarithmic Differentiation to Find the Derivative 56 Finding Derivatives of Functions Involving Exponential Functions 57 Finding Equations of Tangent Lines 58 Finding Equations of Normal Lines 58 Chapter 7: Implicit Differentiation 59 The Problems You''ll Work On 59 What to Watch Out For 59 Using Implicit Differentiation to Find a Derivative 60 Using Implicit Differentiation to Find a Second Derivative 60 Finding Equations of Tangent Lines Using Implicit Differentiation 61 Chapter 8: Applications of Derivatives 63 The Problems You''ll Work On 63 What to Watch Out For 63 Finding and Evaluating Differentials 64 Finding Linearizations 64 Using Linearizations to Estimate Values 64 Understanding Related Rates 65 Finding Maxima and Minima from Graphs 66 Using the Closed Interval Method 67 Finding Intervals of Increase and Decrease 68 Using the First Derivative Test to Find Local Maxima and Minima 68 Determining Concavity 69 Identifying Inflection Points 69 Using the Second Derivative Test to Find Local Maxima and Minima 69 Applying Rolle''s Theorem 70 Using the Mean Value Theorem 70 Applying the Mean Value Theorem to Solve Problems 70 Relating Velocity and Position 71 Finding Velocity and Speed 71 Solving Optimization Problems 72 Doing Approximations Using Newton''s Method 73 Approximating Roots Using Newton''s Method 74 Chapter 9: Areas and Riemann Sums 75 The Problems You''ll Work On 75 What to Watch Out For 75 Calculating Riemann Sums Using Left Endpoints 76 Calculating Riemann Sums Using Right Endpoints 76 Calculating Riemann Sums Using Midpoints 77 Using Limits and Riemann Sums to Find Expressions for Definite Integrals 77 Finding a Definite Integral from the Limit and Riemann Sum Form 78 Using Limits and Riemann Sums to Evaluate Definite Integrals 78 Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem 79 The Problems You''ll Work On 79 What to Watch Out For 80 Using the Fundamental Theorem of Calculus to Find Derivatives 80 Working with Basic Examples of Definite Integrals 81 Understanding Basic Indefinite Integrals 82 Understanding the Net Change Theorem 84 Finding the Displacement of a Particle Given the Velocity 85 Finding the Distance Traveled by a Particle Given the Velocity 85 Finding the Displacement of a Particle Given Acceleration 86 Finding the Distance Traveled by a Particle Given Acceleration 86 Chapter 11: Applications of Integration 87 The Problems You''ll Work On 87 What to Watch Out For 87 Areas between Curves 88 Finding Volumes Using Disks and Washers 89 Finding Volume Using Cross-Sectional Slices 91 Finding Volumes Using Cylindrical Shells 92 Work Problems 94 Average Value of a Function 98 Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L''Hôpital''s Rule 101 The Problems You''ll Work On 101 What to Watch Out For 102 Finding Derivatives Involving Inverse Trigonometric Functions 102 Finding Antiderivatives by Using Inverse Trigonometric Functions 103 Evaluating Hyperbolic Functions Using Their Definitions 104 Finding Derivatives of Hyperbolic Functions 104 Finding Antiderivatives of Hyperbolic Functions 105 Evaluating Indeterminate Forms Using L''Hôpital''s Rule 105 Chapter 13: U-Substitution and Integration by Parts 109 The Problems You''ll Work On 109 What to Watch Out For 109 Using u-Substitutions 110 Using Integration by Parts 111 Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions 115 The Problems You''ll Work On 115 What to Watch Out For 116 Trigonometric Integrals 116 Trigonometric Substitutions 118 Finding Partial Fraction Decompositions (without Coefficients) 119 Finding Partial Fraction Decompositions (Including Coefficients) 120 Integrals Involving Partial Fractions 120 Rationalizing Substitutions 121 Chapter 15: Improper Integrals and More Approximating Techniques 123 The Problems You''ll Work On 123 What to Watch Out For 123 Convergent and Divergent Improper Integrals 124 The Comparison Test for Integrals 125 The Trapezoid Rule 126 Simpson''s Rule 126 Part 2: The Answers 127 Chapter 16: Answers and Explanations 129 Index 581.