Calculus 2nd Edition Rogawski

CONTENTS
CALCULUS
Chapter 1 PRECALCULUS REVIEW 1
1.1 Real Numbers, Functions, and Graphs 1
1.2 Linear and Quadratic Functions 13
1.3 The Basic Classes of Functions 21
1.4 Trigonometric Functions 25
1.5 Technology: Calculators and Computers 33
Chapter 2 LIMITS 40
2.1 Limits, Rates of Change, and Tangent Lines 40
2.2 Limits: A Numerical and Graphical Approach 48
2.3 Basic Limit Laws 58
2.4 Limits and Continuity 62
2.5 Evaluating Limits Algebraically 71
2.6 Trigonometric Limits 76
2.7 Limits at Infinity 81
2.8 Intermediate Value Theorem 87
2.9 The Formal Definition of a Limit 91
Chapter 3 DIFFERENTIATION 101
3.1 Definition of the Derivative 101
3.2 The Derivative as a Function 110
3.3 Product and Quotient Rules 122
3.4 Rates of Change 128
3.5 Higher Derivatives 138
3.6 Trigonometric Functions 144
3.7 The Chain Rule 148
3.8 Implicit Differentiation 157
3.9 Related Rates 163
Chapter 4 APPLICATIONS OF THE DERIVATIVE 175
4.1 Linear Approximation and Applications 175
4.2 Extreme Values 183
4.3 The Mean Value Theorem and Monotonicity 194
4.4 The Shape of a Graph 201
4.5 Graph Sketching and Asymptotes 208
4.6 Applied Optimization 216
4.7 Newton’s Method 228
4.8 Antiderivatives 234
Chapter 5 THE INTEGRAL 244
5.1 Approximating and Computing Area 244
5.2 The Definite Integral 257
vi
5.3 The Fundamental Theorem of Calculus, Part I 267
5.4 The Fundamental Theorem of Calculus, Part II 273
5.5 Net Change as the Integral of a Rate 279
5.6 Substitution Method 285
Chapter 6 APPLICATIONS OF THE INTEGRAL 296
6.1 Area Between Two Curves 296
6.2 Setting Up Integrals: Volume, Density, Average Value 304
6.3 Volumes of Revolution 314
6.4 The Method of Cylindrical Shells 323
6.5 Work and Energy 330
Chapter 7 EXPONENTIAL FUNCTIONS 339
7.1 Derivative of f (x) = b x and the Number e 339
7.2 Inverse Functions 347
7.3 Logarithms and Their Derivatives 355
7.4 Exponential Growth and Decay 364
7.5 Compound Interest and Present Value 371
7.6 Models Involving y ′ = k( y − b) 377
7.7 L’Hôpital’s Rule 382
7.8 Inverse Trigonometric Functions 390
7.9 Hyperbolic Functions 399
Chapter 8 TECHNIQUES OF INTEGRATION 413
8.1 Integration by Parts 413
8.2 Trigonometric Integrals 418
8.3 Trigonometric Substitution 426
8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic
Functions 433
8.5 The Method of Partial Fractions 438
8.6 Improper Integrals 447
8.7 Probability and Integration 459
8.8 Numerical Integration 465
Chapter 9
FURTHER APPLICATIONS OF THE
INTEGRAL AND TAYLOR
POLYNOMIALS 478
9.1 Arc Length and Surface Area 478
9.2 Fluid Pressure and Force 485
9.3 Center of Mass 491
9.4 Taylor Polynomials 499