Precalculus With Limits: Functions and Graphs

by Dugopolski, Mark

• ISBN13: 9780201703337
• ISBN10: 0201703335
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Addison Wesley

Summary

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

Preface	p. vii
List of Supplements	p. xi
Index of Applications	p. xv
Equations, Inequalities, and Modeling
Equations in One Variable	p. 2
Equations and Graphs in Two Variables	p. 12
Scatter Diagrams and Curve Fitting	p. 23
Constructing Models to Solve Problems	p. 29
Quadratic Equations	p. 40
Linear and Absolute Value Inequalities	p. 55
Quadratic and Rational Inequalities	p. 67
Functions and Graphs
Functions	p. 85
Graphs of Relations and Functions	p. 98
Families of Functions: Transformations and Symmetry	p. 109
Operations with Functions	p. 124
Inverse Functions	p. 134
Constructing Functions with Variation	p. 146
Polynomial and Rational Functions
Linear Functions	p. 160
Quadratic Functions	p. 174
Complex Numbers	p. 185
Zeros of Polynomial Functions	p. 192
The Theory of Equations	p. 203
Graphs of Polynomial Functions	p. 212
Graphs of Rational Functions	p. 224
Exponential and Logarithmic Functions
Exponential Functions and Their Applications	p. 246
Logarithmic Functions and Their Applications	p. 261
Properties of Logarithms	p. 273
More Equations and Applications	p. 285
The Trigonometric Functions
Angles and Their Measurements	p. 303
The Sine and Cosine Functions	p. 318
The Graphs of the Sine and Cosine Functions	p. 331
The Other Trigonometric Functions and Their Graphs	p. 348
The Inverse Trigonometric Functions	p. 360
Right Triangle Trigonometry	p. 371
Trigonometric Identities and Conditional Equations
Basic Identities	p. 392
Verifying Identities	p. 400
Sum and Difference Identities	p. 407
Double-Angle and Half-Angle Identities	p. 416
Product and Sum Identities	p. 425
Conditional Trigonometric Equations	p. 434
Applications of Trigonometry
The Law of Sines	p. 453
The Law of Cosines	p. 465
Vectors	p. 474
Trigonometric Form of Complex Numbers	p. 487
Powers and Roots of Complex Numbers	p. 494
Polar Equations	p. 499
Parametric Equations	p. 509
Systems of Equations and Inequalities
Systems of Linear Equations in Two Variables	p. 521
Systems of Linear Equations in Three Variables	p. 532
Nonlinear Systems of Equations	p. 544
Partial Fractions	p. 552
Inequalities and Systems of Inequalities in Two Variables	p. 560
Linear Programming	p. 569
Matrices and Determinants
Solving Linear Systems Using Matrices	p. 580
Operations with Matrices	p. 594
Multiplication of Matrices	p. 600
Inverses of Matrices	p. 608
Solution of Linear Systems in Two Variables Using Determinants	p. 620
Solution of Linear Systems in Three Variables Using Determinants	p. 625
The Conic Sections
The Parabola	p. 639
The Ellipse and the Circle	p. 649
The Hyperbola	p. 662
Rotation of Axes	p. 675
Polar Equations of the Conics	p. 684
Sequences, Series, and Probability
Sequences	p. 695
Series	p. 705
Geometric Sequences and Series	p. 713
Counting and Permutations	p. 725
Combinations, Labeling, and the Binomial Theorem	p. 732
Probability	p. 741
Mathematical Induction	p. 751
Analytic Geometry and Vectors in Three Dimensions
Graphs in Space	p. 763
Vectors in Space	p. 768
Cross Product and Scalar Triple Product	p. 775
Equations of Lines and Planes in Space	p. 782
Limits
Finding Limits Numerically and Graphically	p. 796
Finding Limits Algebraically with Limit Theorems	p. 804
One-Sided Limits, Continuity, and Limits Involving Infinity	p. 811
Tangent Lines and the Derivative	p. 819
Appendix: Basic Algebra Review	p. 1
Real Numbers and Their Properties	p. 1
Exponents and Radicals	p. 8
Polynomials	p. 18
Factoring Polynomials	p. 23
Rational Expressions	p. 28
Appendix: Techniques for Solving Miscellaneous Equations	p. 35
Answers to Selected Exercises	p. 1
Credits	p. 1
Index	p. 1
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