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)*