Precalculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Pearson
8 2023]
|
| Ausgabe: | 7th edition, global edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 1357 Seiten Illustrationen, Diagramme |
| ISBN: | 9781292730967 129273096X |
Internformat
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Datensatz im Suchindex
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Contents Preface 9 To the Student 19 About the Author 20 Applications Index 21 P Fundamental Concepts of Algebra 29 P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 30 P.2 Exponents and Scientific Notation 48 P.3 Radicals and Rational Exponents 60 P.4 Polynomials 76 P.5 Factoring Polynomials 85 Mid-Chapter Check Point 97 P.6 Rational Expressions 98 P.7 Equations 116 P.8 Models and Applications 138 P.9 Linear Inequalities and Absolute Value Inequalities 154 Summary, Review, and Test 170 Review Exercises 171 Chapter P Test 174 1 Functions and Graphs 177 1.1 Graphs and Graphing Utilities 178 1.2 Basics of Functions and Their Graphs 191 1.3 More on Functions and Their Graphs 210 1.4 Linear Functions and Slope 230 1.5 More on Slope 246 Mid-Chapter Check Point 257 1.6 Transformations of Functions 258 1.7 Combinations of Functions; Composite Functions 274 1.8 Inverse Functions 289 1.9 Distance and Midpoint Formulas; Circles 300 1.10 Modeling with Functions 310 Summary, Review, and Test 324 Review Exercises 328 Chapter 1 Test 333
3.4 Exponential and Logarithmic Equations 508 3.5 Exponential Growth and Decay; Modeling Data 523 Summary, Review, and Test 539 Review Exercises 541 Chapters Test 545 Cumulative Review Exercises (Chapters P-3) 546 4 Trigonometric Functions 549 4.1 Angles and Radian Measure 550 4.2 Trigonometric Functions: The Unit Circle 567 4.3 Right Triangle Trigonometry 583 4.4 Trigonometric Functions of Any Angle 596 Mid-Chapter Check Point 609 2 Polynomial and Rational Functions 337 2.1 Complex Numbers 338 2.2 Quadratic Functions 347 2.3 Polynomial Functions and Their Graphs 365 2.4 Dividing Polynomials; Remainder and Factor Theorems 383 2.5 Zeros of Polynomial Functions 396 4.5 Graphs of Sine and Cosine Functions 611 4.6 Graphs of Other Trigonometric Functions 632 4.7 Inverse Trigonometric Functions 646 4.8 Applications of Trigonometric Functions 664 Summary, Review, and Test 675 Review Exercises 679 Chapter 4 Test 682 Cumulative Review Exercises (Chapters P-4) 683 Mid-Chapter Check Point 410 2.6 Rational Functions and Their Graphs 412 2.7 Polynomial and Rational Inequalities 434 2.8 Modeling Using Variation 447 Summary, Review, and Test 457 Review Exercises 460 Chapter 2 Test 464 Cumulative Review Exercises (Chapters P-2) 466 3 Exponential and Logarithmic Functions 467 * 3.1 Exponential Functions 468 3.2 Logarithmic Functions 482 3.3 Properties of Logarithms 497 Mid-Chapter Check Point 507 t-
Contents 5 Analytic Trigonometry 685 5.1 Verifying Trigonometric Identities 686 5.2 Sum and Difference Formulas 698 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 709 7.5 Systems of Inequalities 894 7.6 Linear Programming 907 Summary, Review, and Test 914 Review Exercises 916 Chapter 7 Test 919 Cumulative Review Exercises (Chapters P-7) 919 Mid-Chapter Check Point 720 5.4 Product-to-Sum and Sum-to-Product Formulas 721 5.5 Trigonometric Equations 730 Summary, Review, and Test 745 Review Exercises 746 Chapter 5 Test 748 Cumulative Review Exercises (Chapters P-5) 749 6 Additional Topics in Trigonometry 751 6.1 The Law of Sines 752 6.2 The Law of Cosines 764 6.3 Polar Coordinates 773 6.4 Graphs of Polar Equations 785 Mid-Chapter Check Point 796 6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem 797 6.6 Vectors 810 6.7 The Dot Product 825 Summary, Review, and Test 835 Review Exercises 838 Chapter 6 Test 840 Cumulative Review Exercises (Chapters P-6) 841 7 Systems of Equations and Inequalities 843 7.1 Systems of Linear Equations in Two Variables 844 7.2 Systems of Linear Equations in Three Variables 864 7.3 Partial Fractions 872 7.4 Systems of Nonlinear Equations in Two Variables 883 Mid-Chapter Check Point 893 8 Matrices and Determinants 921 8.1 Matrix Solutions to Linear Systems 922 8.2 Inconsistent and Dependent Systems and Their Applications 936 8.3 Matrix Operations and Their Applications 945 Mid-Chapter Check Point 960 8.4 Multiplicative Inverses of Matrices and Matrix Equations 961 8.5 Determinants and Cramer’s Rule 975 Summary, Review, and Test 988 Review
Exercises 990 Chapter 8 Test 992 Cumulative Review Exercises (Chapters P-8) 993 7
8 9 Contents Conic Sections and Analytic Geometry 995 I «4 I Introduction to Calculus 1171 9.1 The Ellipse 996 11.1 Finding Limits Using Tables and Graphs 1172 9.2 The Hyperbola 1011 11.2 Finding Limits Using Properties of Limits 1184 9.3 The Parabola 1026 11.3 Limits and Continuity 1198 Mid-Chapter Check Point 1040 Mid-Chapter Check Point 1205 9.4 Rotation of Axes 1042 11.4 Introduction to Derivatives 1206 9.5 Parametric Equations 1053 Summary, Review, and Test 1219 9.6 Conic Sections in Polar Coordinates 1063 Review Exercises 1220 Summary, Review, and Test 1073 Chapter 11 Test 1222 Review Exercises 1076 Cumulative Review Exercises (Chapters P-11) 1222 Chapter 9 Test 1078 Cumulative Review Exercises (Chapters P-9) 1079 Appendix A: Where Did That Come From? Selected Proofs 1225 Appendix B: The Transition from Precalculus to Calculus 1231 Sequences, Induction, and Probability 1081 10.1 Sequences and Summation Notation 1082 10.2 Arithmetic Sequences 1093 10.3 Geometric Sequences and Series 1104 Mid-Chapter Check Point 1119 10.4 Mathematical Induction 1120 10.5 The Binomial Theorem 1129 10.6 Counting Principles, Permutations, and Combinations 1137 10.7 Probability 1148 Summary, Review, and Test 1163 Review Exercises 1166 Chapter 10 Test 1168 Cumulative Review Exercises (Chapters P-10) 1169 Answers to Selected Exercises 1233 Subject Index 1340 Credits 1357 |
| adam_txt |
Contents Preface 9 To the Student 19 About the Author 20 Applications Index 21 P Fundamental Concepts of Algebra 29 P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 30 P.2 Exponents and Scientific Notation 48 P.3 Radicals and Rational Exponents 60 P.4 Polynomials 76 P.5 Factoring Polynomials 85 Mid-Chapter Check Point 97 P.6 Rational Expressions 98 P.7 Equations 116 P.8 Models and Applications 138 P.9 Linear Inequalities and Absolute Value Inequalities 154 Summary, Review, and Test 170 Review Exercises 171 Chapter P Test 174 1 Functions and Graphs 177 1.1 Graphs and Graphing Utilities 178 1.2 Basics of Functions and Their Graphs 191 1.3 More on Functions and Their Graphs 210 1.4 Linear Functions and Slope 230 1.5 More on Slope 246 Mid-Chapter Check Point 257 1.6 Transformations of Functions 258 1.7 Combinations of Functions; Composite Functions 274 1.8 Inverse Functions 289 1.9 Distance and Midpoint Formulas; Circles 300 1.10 Modeling with Functions 310 Summary, Review, and Test 324 Review Exercises 328 Chapter 1 Test 333
3.4 Exponential and Logarithmic Equations 508 3.5 Exponential Growth and Decay; Modeling Data 523 Summary, Review, and Test 539 Review Exercises 541 Chapters Test 545 Cumulative Review Exercises (Chapters P-3) 546 4 Trigonometric Functions 549 4.1 Angles and Radian Measure 550 4.2 Trigonometric Functions: The Unit Circle 567 4.3 Right Triangle Trigonometry 583 4.4 Trigonometric Functions of Any Angle 596 Mid-Chapter Check Point 609 2 Polynomial and Rational Functions 337 2.1 Complex Numbers 338 2.2 Quadratic Functions 347 2.3 Polynomial Functions and Their Graphs 365 2.4 Dividing Polynomials; Remainder and Factor Theorems 383 2.5 Zeros of Polynomial Functions 396 4.5 Graphs of Sine and Cosine Functions 611 4.6 Graphs of Other Trigonometric Functions 632 4.7 Inverse Trigonometric Functions 646 4.8 Applications of Trigonometric Functions 664 Summary, Review, and Test 675 Review Exercises 679 Chapter 4 Test 682 Cumulative Review Exercises (Chapters P-4) 683 Mid-Chapter Check Point 410 2.6 Rational Functions and Their Graphs 412 2.7 Polynomial and Rational Inequalities 434 2.8 Modeling Using Variation 447 Summary, Review, and Test 457 Review Exercises 460 Chapter 2 Test 464 Cumulative Review Exercises (Chapters P-2) 466 3 Exponential and Logarithmic Functions 467 * 3.1 Exponential Functions 468 3.2 Logarithmic Functions 482 3.3 Properties of Logarithms 497 Mid-Chapter Check Point 507 t-
Contents 5 Analytic Trigonometry 685 5.1 Verifying Trigonometric Identities 686 5.2 Sum and Difference Formulas 698 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 709 7.5 Systems of Inequalities 894 7.6 Linear Programming 907 Summary, Review, and Test 914 Review Exercises 916 Chapter 7 Test 919 Cumulative Review Exercises (Chapters P-7) 919 Mid-Chapter Check Point 720 5.4 Product-to-Sum and Sum-to-Product Formulas 721 5.5 Trigonometric Equations 730 Summary, Review, and Test 745 Review Exercises 746 Chapter 5 Test 748 Cumulative Review Exercises (Chapters P-5) 749 6 Additional Topics in Trigonometry 751 6.1 The Law of Sines 752 6.2 The Law of Cosines 764 6.3 Polar Coordinates 773 6.4 Graphs of Polar Equations 785 Mid-Chapter Check Point 796 6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem 797 6.6 Vectors 810 6.7 The Dot Product 825 Summary, Review, and Test 835 Review Exercises 838 Chapter 6 Test 840 Cumulative Review Exercises (Chapters P-6) 841 7 Systems of Equations and Inequalities 843 7.1 Systems of Linear Equations in Two Variables 844 7.2 Systems of Linear Equations in Three Variables 864 7.3 Partial Fractions 872 7.4 Systems of Nonlinear Equations in Two Variables 883 Mid-Chapter Check Point 893 8 Matrices and Determinants 921 8.1 Matrix Solutions to Linear Systems 922 8.2 Inconsistent and Dependent Systems and Their Applications 936 8.3 Matrix Operations and Their Applications 945 Mid-Chapter Check Point 960 8.4 Multiplicative Inverses of Matrices and Matrix Equations 961 8.5 Determinants and Cramer’s Rule 975 Summary, Review, and Test 988 Review
Exercises 990 Chapter 8 Test 992 Cumulative Review Exercises (Chapters P-8) 993 7
8 9 Contents Conic Sections and Analytic Geometry 995 I «4 I Introduction to Calculus 1171 9.1 The Ellipse 996 11.1 Finding Limits Using Tables and Graphs 1172 9.2 The Hyperbola 1011 11.2 Finding Limits Using Properties of Limits 1184 9.3 The Parabola 1026 11.3 Limits and Continuity 1198 Mid-Chapter Check Point 1040 Mid-Chapter Check Point 1205 9.4 Rotation of Axes 1042 11.4 Introduction to Derivatives 1206 9.5 Parametric Equations 1053 Summary, Review, and Test 1219 9.6 Conic Sections in Polar Coordinates 1063 Review Exercises 1220 Summary, Review, and Test 1073 Chapter 11 Test 1222 Review Exercises 1076 Cumulative Review Exercises (Chapters P-11) 1222 Chapter 9 Test 1078 Cumulative Review Exercises (Chapters P-9) 1079 Appendix A: Where Did That Come From? Selected Proofs 1225 Appendix B: The Transition from Precalculus to Calculus 1231 Sequences, Induction, and Probability 1081 10.1 Sequences and Summation Notation 1082 10.2 Arithmetic Sequences 1093 10.3 Geometric Sequences and Series 1104 Mid-Chapter Check Point 1119 10.4 Mathematical Induction 1120 10.5 The Binomial Theorem 1129 10.6 Counting Principles, Permutations, and Combinations 1137 10.7 Probability 1148 Summary, Review, and Test 1163 Review Exercises 1166 Chapter 10 Test 1168 Cumulative Review Exercises (Chapters P-10) 1169 Answers to Selected Exercises 1233 Subject Index 1340 Credits 1357 |
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