## Precalculus with Limits, Fifth Edition

By Ron Larson

**Contents:**

1. Functions and Their Graphs 1

1.1 Rectangular Coordinates 2

1.2 Graphs of Equations 11

1.3 Linear Equations in Two Variables 22

1.4 Functions 35

1.5 Analyzing Graphs of Functions 49

1.6 A Library of Parent Functions 60

1.7 Transformations of Functions 67

1.8 Combinations of Functions: Composite Functions 76

1.9 Inverse Functions 84

1.10 Mathematical Modeling and Variation 93

Summary and Study Strategies 104

Review Exercises 106

Chapter Test 109

Proofs in Mathematics 110

P.S. Problem Solving 111

2. Polynomial and Rational Functions 113

2.1 Quadratic Functions and Models 114

2.2 Polynomial Functions of Higher Degree 123

2.3 Polynomial and Synthetic Division 136

2.4 Complex Numbers 145

2.5 Zeros of Polynomial Functions 152

2.6 Rational Functions 166

2.7 Nonlinear Inequalities 178

Summary and Study Strategies 188

Review Exercises 190

Chapter Test 192

Proofs in Mathematics 193

P.S. Problem Solving 195

3. Exponential and Logarithmic Functions 197

3.1 Exponential Functions and Their Graphs 198

3.2 Logarithmic Functions and Their Graphs 209

3.3 Properties of Logarithms 219

3.4 Exponential and Logarithmic Equations 226

3.5 Exponential and Logarithmic Models 236

Summary and Study Strategies 248

Review Exercises 250

Chapter Test 253

Cumulative Test for Chapters 1–3 254

Proofs in Mathematics 256

P.S. Problem Solving 257

4. Trigonometry 259

4.1 Radian and Degree Measure 260

4.2 Trigonometric Functions: The Unit Circle 270

4.3 Right Triangle Trigonometry 277

4.4 Trigonometric Functions of Any Angle 288

4.5 Graphs of Sine and Cosine Functions 297

4.6 Graphs of Other Trigonometric Functions 308

4.7 Inverse Trigonometric Functions 318

4.8 Applications and Models 328

Summary and Study Strategies 338

Review Exercises 340

Chapter Test 343

Proofs in Mathematics 344

P.S. Problem Solving 345

5. Analytic Trigonometry 347

5.1 Using Fundamental Identities 348

5.2 Verifying Trigonometric Identities 355

5.3 Solving Trigonometric Equations 362

5.4 Sum and Difference Formulas 374

5.5 Multiple-Angle and Product-to-Sum Formulas 381

Summary and Study Strategies 390

Review Exercises 392

Chapter Test 394

Proofs in Mathematics 395

P.S. Problem Solving 397

6. Additional Topics in Trigonometry 399

6.1 Law of Sines 400

6.2 Law of Cosines 409

6.3 Vectors in the Plane 416

6.4 Vectors and Dot Products 429

6.5 The Complex Plane 438

6.6 Trigonometric Form of a Complex Number 445

Summary and Study Strategies 454

Review Exercises 456

Chapter Test 459

Cumulative Test for Chapters 4–6 460

Proofs in Mathematics 462

P.S. Problem Solving 465

7. Systems of Equations and Inequalities 467

7.1 Linear and Nonlinear Systems of Equations 468

7.2 Two-Variable Linear Systems 478

7.3 Multivariable Linear Systems 490

7.4 **Partial Fractions** 502

7.5 Systems of Inequalities 510

7.6 Linear Programming 520

Summary and Study Strategies 529

Review Exercises 531

Chapter Test 535

Proofs in Mathematics 536

8. Matrices and Determinants 539

8.1 Matrices and Systems of Equations 540

8.2 Operations with Matrices 553

8.3 The Inverse of a Square Matrix 568

8.4 The Determinant of a Square Matrix 577

8.5 Applications of Matrices and Determinants 585

Summary and Study Strategies 598

Review Exercises 600

Chapter Test 604

Proofs in Mathematics 605

P.S. Problem Solving 607

9. Sequences, Series, and Probability 609

9.1 Sequences and Series 610

9.2 Arithmetic Sequences and Partial Sums 620

9.3 Geometric Sequences and Series 629

9.4 Mathematical Induction 638

9.5 The Binomial Theorem 648

9.6 Counting Principles 656

9.7 Probability 666

Summary and Study Strategies 678

Review Exercises 680

Chapter Test 683

Cumulative Test for Chapters 7–9 684

Proofs in Mathematics 686

P.S. Problem Solving 689

10. Topics in Analytic Geometry 691

10.1 Lines 692

10.2 Introduction to Conics: Parabolas 699

10.3 Ellipses 708

10.4 Hyperbolas 717

10.5 Rotation of Conics 727

10.6 Parametric Equations 735

10.7 Polar Coordinates 745

10.8 Graphs of Polar Equations 751

10.9 Polar Equations of Conics 759

Summary and Study Strategies 766

Review Exercises 768

Chapter Test 771

Proofs in Mathematics 772

P.S. Problem Solving 775

11. Analytic Geometry in Three Dimensions 777

11.1 The Three-Dimensional **Coordinate System** 778

11.2 Vectors in Space 785

11.3 The Cross Product of Two Vectors 792

11.4 Lines and Planes in Space 799

Summary and Study Strategies 808

Review Exercises 810

Chapter Test 812

Proofs in Mathematics 813

P.S. Problem Solving 815

12. Limits and an Introduction to Calculus 817

12.1 Introduction to Limits 818

12.2 Techniques for Evaluating Limits 829

12.3 The Tangent Line Problem 839

12.4 Limits at Infinity and Limits of Sequences 849

12.5 The Area Problem 858

Summary and Study Strategies 866

Review Exercises 868

Chapter Test 871

Cumulative Test for Chapters 10–12 872

Proofs in Mathematics 874

P.S. Problem Solving 875

13. Concepts in Statistics 877

13.1 Representing Data 878

13.2 Analyzing Data 885

13.3 Modeling Data 897

Summary and Study Strategies 904

Review Exercises 906

Chapter Test 908

Proofs in Mathematics 909

P.S. Problem Solving 910

Appendix A

Appendix A: Review of Fundamental Concepts of Algebra

A.1 Real Numbers and Their Properties A1

A.2 Exponents and Radicals A13

A.3 Polynomials and Factoring A25

A.4 Rational Expressions A35

A.5 Solving Equations A45

A.6 Linear Inequalities in One Variable A58

A.7 Errors and the Algebra of Calculus A67

Answers to Odd-Numbered Exercises and Tests A75

Index A200

Index of Applications (online)*