The Calculus, with Analytic Geometry

REAL NUMBERS,

INTRODUCTION TO

ANALYTIC GEOMETRY,

AND FUNCTIONS

page 1

Chapter 2

LIMITS AND CONTINUIT}

paSe oc

Chapter 3

THE DERIVATIVE

page 110

Preface )cu,

1.1 Sets, Real Numbers, and Inequalities 2

1.2 Absolute Value 14

1.3 The Number Plane and Graphs of Equations 2L

1.4 Distance Formula and Midpoint Formula 28

1.5 Equations of a Line 33

1.6 The Circle 43

L.7 Functions and Their Graphs 48

1.8 Function Notation, Operations on Functions, and Types of Func-

tions 56

2.1, The Limit of a Function 66

2.2 Theorems on Limits of Functions 74

2.3 One-Sided Limits 85

2.4 Infinite Limits 88

2.5 Continuity of a Function at a Number 97

2.6 Theorems on Continuity 1-0L

3.1 The Tangent Line 1-1-i-

3.2 Instantaneous Velocity in Rectilinear Motion 11,5

3.3 The Derivative of a Function L21-

3.4 Differentiability and Continuity L26

3.5 Some Theorems on Differentiation of Algebraic Functions 1.30

3.6 The Derivative of a Composite Function L38

3.7 The Derivative of the Power Function for Rational Exponents L42

3.8 Implicit Differentiation 1-45

3.9 The Derivative as a Rate of Change 1.50

3.10 Related Rates 154

3.1L Derivatives of Higher Order 157Chapter 4

TOPICS ON LIMITS,

CONTINUITY, AND THE

DERIVATIVE

page 164

Chapter 5

ADDITIONAT APPLICATIONS

OF THE DERIVATIVE

page 204

Chapter 5

THE DIFFERENTIAL AND

ANTIDIFFERENTIATION

page 243

Chapter 7

THE DEFINITE INTEGRAL

page 275

Chapter 8

APPLICATIONS OF THE

DEFINITE INTEGRAL

page 323

5.1 The Differential 244

6.2 Differential Formulas 249

5.3 The Inverse of Differentiation 253

6.4 Differential Equations with Variables Separable

6.5 Antidifferentiation and Rectilinear Motion 265

6.6 Applications of Antidifferentiation in Economics

4.L Limits at Infinity 765

4.2 Horizontal and Vertical Asymptotes L71

4.3 Additional Theorems on Limits of Functions 1.74

4.4 Continuity on an Interval 177

4.5 Maximum and Minimum Values of a Function 19L

4.6 Applications Involving an Absolute Extremum on a Closed In-

terval L89

4.7 Rolle's Theorem and the