Page 9 - Calculus Demystified

viii
81
CHAPTER 3 Applications of the Derivative Contents
3.1 Graphing of Functions 81
3.2 Maximum/Minimum Problems 86
3.3 Related Rates 91
3.4 Falling Bodies 94

CHAPTER 4 The Integral 99

4.0 Introduction 99
4.1 Antiderivatives and Indefinite Integrals 99
4.1.1 The Concept of Antiderivative 99
4.1.2 The Indefinite Integral 100
4.2 Area 103
4.3 Signed Area 111
4.4 The Area Between Two Curves 116
4.5 Rules of Integration 120
4.5.1 Linear Properties 120
4.5.2 Additivity 120

CHAPTER 5 Indeterminate Forms 123
5.1 l’Hôpital’s Rule 123
5.1.1 Introduction 123
5.1.2 l’Hôpital’s Rule 124
5.2 Other Indeterminate Forms 128
5.2.1 Introduction 128
5.2.2 Writing a Product as a Quotient 128
5.2.3 The Use of the Logarithm 128
5.2.4 Putting Terms Over a Common Denominator 130
5.2.5 Other Algebraic Manipulations 131
5.3 Improper Integrals: A First Look 132
5.3.1 Introduction 132
5.3.2 Integrals with Infinite Integrands 133
5.3.3 An Application to Area 139
5.4 More on Improper Integrals 140
5.4.1 Introduction 140
5.4.2 The Integral on an Infinite Interval 141
5.4.3 Some Applications 143