Precalculus With Limits: Functions and Graphs

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2002-01-01
  • Publisher: Addison Wesley

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Supplemental Materials

What is included with this book?


Building on Mark Dugopolski's name, this graphing optional text is designed for the one or two semester precalculus course and includes coverage of analytic geometry, vectors, and the limit. With faster pacing and less review, this is an excellent choice for those students going on to calculus.

Table of Contents

Prefacep. vii
List of Supplementsp. xi
Index of Applicationsp. xv
Equations, Inequalities, and Modeling
Equations in One Variablep. 2
Equations and Graphs in Two Variablesp. 12
Scatter Diagrams and Curve Fittingp. 23
Constructing Models to Solve Problemsp. 29
Quadratic Equationsp. 40
Linear and Absolute Value Inequalitiesp. 55
Quadratic and Rational Inequalitiesp. 67
Functions and Graphs
Functionsp. 85
Graphs of Relations and Functionsp. 98
Families of Functions: Transformations and Symmetryp. 109
Operations with Functionsp. 124
Inverse Functionsp. 134
Constructing Functions with Variationp. 146
Polynomial and Rational Functions
Linear Functionsp. 160
Quadratic Functionsp. 174
Complex Numbersp. 185
Zeros of Polynomial Functionsp. 192
The Theory of Equationsp. 203
Graphs of Polynomial Functionsp. 212
Graphs of Rational Functionsp. 224
Exponential and Logarithmic Functions
Exponential Functions and Their Applicationsp. 246
Logarithmic Functions and Their Applicationsp. 261
Properties of Logarithmsp. 273
More Equations and Applicationsp. 285
The Trigonometric Functions
Angles and Their Measurementsp. 303
The Sine and Cosine Functionsp. 318
The Graphs of the Sine and Cosine Functionsp. 331
The Other Trigonometric Functions and Their Graphsp. 348
The Inverse Trigonometric Functionsp. 360
Right Triangle Trigonometryp. 371
Trigonometric Identities and Conditional Equations
Basic Identitiesp. 392
Verifying Identitiesp. 400
Sum and Difference Identitiesp. 407
Double-Angle and Half-Angle Identitiesp. 416
Product and Sum Identitiesp. 425
Conditional Trigonometric Equationsp. 434
Applications of Trigonometry
The Law of Sinesp. 453
The Law of Cosinesp. 465
Vectorsp. 474
Trigonometric Form of Complex Numbersp. 487
Powers and Roots of Complex Numbersp. 494
Polar Equationsp. 499
Parametric Equationsp. 509
Systems of Equations and Inequalities
Systems of Linear Equations in Two Variablesp. 521
Systems of Linear Equations in Three Variablesp. 532
Nonlinear Systems of Equationsp. 544
Partial Fractionsp. 552
Inequalities and Systems of Inequalities in Two Variablesp. 560
Linear Programmingp. 569
Matrices and Determinants
Solving Linear Systems Using Matricesp. 580
Operations with Matricesp. 594
Multiplication of Matricesp. 600
Inverses of Matricesp. 608
Solution of Linear Systems in Two Variables Using Determinantsp. 620
Solution of Linear Systems in Three Variables Using Determinantsp. 625
The Conic Sections
The Parabolap. 639
The Ellipse and the Circlep. 649
The Hyperbolap. 662
Rotation of Axesp. 675
Polar Equations of the Conicsp. 684
Sequences, Series, and Probability
Sequencesp. 695
Seriesp. 705
Geometric Sequences and Seriesp. 713
Counting and Permutationsp. 725
Combinations, Labeling, and the Binomial Theoremp. 732
Probabilityp. 741
Mathematical Inductionp. 751
Analytic Geometry and Vectors in Three Dimensions
Graphs in Spacep. 763
Vectors in Spacep. 768
Cross Product and Scalar Triple Productp. 775
Equations of Lines and Planes in Spacep. 782
Finding Limits Numerically and Graphicallyp. 796
Finding Limits Algebraically with Limit Theoremsp. 804
One-Sided Limits, Continuity, and Limits Involving Infinityp. 811
Tangent Lines and the Derivativep. 819
Appendix: Basic Algebra Reviewp. 1
Real Numbers and Their Propertiesp. 1
Exponents and Radicalsp. 8
Polynomialsp. 18
Factoring Polynomialsp. 23
Rational Expressionsp. 28
Appendix: Techniques for Solving Miscellaneous Equationsp. 35
Answers to Selected Exercisesp. 1
Creditsp. 1
Indexp. 1
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