Precalculus

by Larson, Ron

• ISBN13: 9780669417418
• ISBN10: 0669417416
• Edition: 4th
• Format: Paperback
• Copyright: 1996-11-01
• Publisher: Brooks Cole

Table of Contents

Prerequisites	1	(102)
Real Numbers	2	(11)
Exponents and Radicals	13	(14)
Polynomials and Factoring	27	(14)
Fractional Expressions	41	(11)
Solving Equations	52	(13)
Solving Inequalities	65	(12)
Errors and the Algebra of Calculus	77	(8)
Graphical Representation of Data	85	(18)
Focus on Concepts	95	(1)
Review Exercises	96	(4)
Chapter Project: A Numerical Approach to Maximizing a Volume	100	(2)
Chapter Test	102	(1)
Functions and Their Graphs	103	(102)
Graphs and Graphing Utilities	104	(14)
Lines in the Plane and Slope	118	(15)
Functions	133	(14)
Analyzing Graphs of Functions	147	(12)
Translations and Combinations	159	(14)
Inverse Functions	173	(11)
Mathematical Modeling	184	(21)
Focus on Concepts	198	(1)
Review Exercises	199	(3)
Chapter Project: A Graphical Approach to Maximization	202	(2)
Chapter Test	204	(1)
Polynomial and Rational Functions	205	(92)
Quadratic Functions	206	(12)
Polynomial Functions of Higher Degree	218	(13)
Polynomial and Synthetic Division	231	(11)
Real Zeros of Polynomial Functions	242	(10)
Complex Numbers	252	(8)
The Fundamental Theorem of Algebra	260	(9)
Rational Functions	269	(13)
Partial Fractions	282	(15)
Focus on Concepts	290	(1)
Review Exercises	291	(3)
Chapter Project: A Graphical Approach to Finding Zeros	294	(2)
Chapter Test	296	(1)
Exponential and Logarithmic Functions	297	(62)
Exponential Functions and Their Graphs	298	(12)
Logarithmic Functions and Their Graphs	310	(11)
Properties of Logarithms	321	(7)
Exponential and Logarithmic Equations	328	(11)
Exponential and Logarithmic Models	339	(20)
Focus on Concepts	352	(1)
Review Exercises	353	(3)
Chapter Project: A Graphical Approach to Compound Interest	356	(2)
Cumulative Test for Chapters 1--3	358	(1)
Trigonometry	359	(98)
Radian and Degree Measure	360	(11)
Trigonometric Functions: The Unit Circle	371	(9)
Right Triangle Trigonometry	380	(12)
Trigonometric Functions of Any Angle	392	(10)
Graphs of Sine and Cosine Functions	402	(13)
Graphs of Other Trigonometric Functions	415	(12)
Inverse Trigonometric Functions	427	(11)
Applications and Models	438	(19)
Focus on Concepts	450	(1)
Review Exercises	451	(3)
Chapter Project: Analyzing a Graph	454	(2)
Chapter Test	456	(1)
Analytic Trigonometry	457	(54)
Using Fundamental Identities	458	(8)
Verifying Trigonometric Identities	466	(8)
Solving Trigonometric Equations	474	(11)
Sum and Difference Formulas	485	(8)
Multiple-Angle and Product-to-Sum Formulas	493	(18)
Focus on Concepts	505	(1)
Review Exercises	506	(2)
Chapter Project: Solving Equations Graphically	508	(2)
Chapter Test	510	(1)
Additional Topics in Trigonometry	511	(62)
Law of Sines	512	(10)
Law of Cosines	522	(9)
Vectors in a Plane	531	(14)
Vectors and Dot Products	545	(10)
DeMoivre's Theorem	555	(18)
Focus on Concepts	566	(1)
Review Exercises	567	(3)
Chapter Project: Adding Vectors Graphically	570	(2)
Cumulative Test for Chapters 4--6	572	(1)
Systems of Equations and Inequalities	573	(66)
Solving Systems of Equations	574	(11)
Two-Variable Linear Systems	585	(12)
Multivariable Linear Systems	597	(13)
Systems of Inequalities	610	(10)
Linear Programming	620	(19)
Focus on Concepts	631	(1)
Review Exercises	632	(4)
Chapter Project: Fitting Models to Data	636	(2)
Chapter Test	638	(1)
Matrices and Determinants	639	(68)
Matrices and Systems of Equations	640	(15)
Operations with Matrices	655	(14)
The Inverse of a Square Matrix	669	(10)
The Determinant of a Square Matrix	679	(9)
Applications of Matrices and Determinants	688	(19)
Focus on Concepts	700	(1)
Review Exercises	701	(3)
Chapter Project: Solving Systems of Equations	704	(2)
Chapter Test	706	(1)
Sequences and Probability	707	(82)
Sequences and Summation Notation	708	(12)
Arithmetic Sequences	720	(9)
Geometric Sequences	729	(10)
Mathematical Induction	739	(11)
The Binomial Theorem	750	(8)
Counting Principles	758	(10)
Probability	768	(21)
Focus on Concepts	782	(1)
Review Exercises	783	(3)
Chapter Project: Recognizing Patterns in Data	786	(2)
Cumulative Test for Chapters 7-9	788	(1)
Topics in Analytic Geometry	789	(1)
Lines	790	(8)
Introduction to Conics: Parabolas	798	(9)
Ellipses	807	(10)
Hyperbolas	817	(10)
Rotation of Conics	827	(9)
Parametric Equations	836	(10)
Polar Coordinates	846	(8)
Graphs of Polar Equations	854	(9)
Polar Equations of Conics	863	(5)
Focus on Concepts	872	(1)
Review Exercises	873	(3)
Chapter Project: Graphing in Parametric and Polar Models	876	(2)
Chapter Test	878
APPENDICES	A1
Appendix A: Further Concepts in Statistics	A2
A.1 Representing Data and Linear Modeling	A2
A.2 Measures of Central Tendency and Dispersion	A13
Appendix B: Think About the Proof	A21
Appendix C: Programs	A31
Appendix D: Scientific Calculator Keystrokes	A69
Answers to Warm UPS, Odd-Numbered Exercises, Focus on Concepts, and Tests	A73
Index of Applications	A193
Index	A198