Precalculus with Limits A Graphing Approach

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618052912
• ISBN10: 0618052917
• Edition: 3rd
• Format: Hardcover
• Copyright: 2000-08-04
• Publisher: Brooks Cole

Summary

For a full description, see Larson et al., College Algebra: A Graphing Approach, 3/e.

Table of Contents

A Word from the Authors (Preface)	viii
Features Highlights	xi
An Introduction to Graphing Utilities	xvii
Prerequisites	1	(72)
Graphical Representation of Data	2	(12)
Graphs of Equations	14	(11)
Lines in the Plane	25	(13)
Solving Equations Algebraically and Graphically	38	(16)
Solving Inequalities Algebraically and Graphically	54	(19)
Chapter Summary	66	(1)
Review Exercises	67	(3)
Chapter Project: Modeling the Volume of a Box	70	(1)
Chapter Test	71	(1)
Library of Functions	72	(1)
Functions and Their Graphs	73	(62)
Functions	74	(14)
Graphs of Functions	88	(12)
Shifting, Reflecting, and Stretching Graphs	100	(9)
Combinations of Functions	109	(11)
Inverse Functions	120	(15)
Chapter Summary	130	(1)
Review Exercises	131	(2)
Chapter Project: Modeling the Area of a Plot	133	(1)
Chapter Test	134	(1)
Polynomial and Rational Functions	135	(80)
Quadratic Functions	136	(11)
Polynomial Functions of Higher Degree	147	(13)
Real Zeros of Polynomial Functions	160	(14)
Complex Numbers	174	(8)
The Fundamental Theorem of Algebra	182	(7)
Rational Functions and Asymptotes	189	(10)
Graphs of Rational Functions	199	(16)
Chapter Summary	208	(1)
Review Exercises	209	(4)
Chapter Project: Finding Points of Intersection	213	(1)
Chapter Test	214	(1)
Exponential and Logarithmic Functions	215	(68)
Exponential Functions and Their Graphs	216	(13)
Logarithmic Functions and Their Graphs	229	(11)
Properties of Logarithms	240	(7)
Solving Exponential and Logarithmic Equations	247	(11)
Exponential and Logarithmic Models	258	(25)
Chapter Summary	274	(1)
Review Exercises	275	(4)
Chapter Project: A Graphical Approach to Compound Interest	279	(1)
Chapter Test	280	(1)
Cumulative Test: Chapters 1--3	281	(2)
Trigonometric Functions	283	(92)
Radian and Degree Measure	284	(11)
Trigonometric Functions: The Unit Circle	295	(8)
Right Triangle Trigonometry	303	(11)
Trigonometric Functions of Any Angle	314	(9)
Graphs of Sine and Cosine Functions	323	(11)
Graphs of Other Trigonometric Functions	334	(11)
Inverse Trigonometric Functions	345	(10)
Applications and Models	355	(20)
Chapter Summary	367	(1)
Review Exercises	368	(5)
Chapter Project: Fitting a Model to Data	373	(1)
Chapter Test	374	(1)
Analytic Trigonometry	375	(52)
Using Fundamental Identities	376	(8)
Verifying Trigonometric Identities	384	(8)
Solving Trigonometric Equations	392	(12)
Sum and Difference Formulas	404	(7)
Multiple-Angle and Product-Sum Formulas	411	(16)
Chapter Summary	421	(1)
Review Exercises	422	(3)
Chapter Project: Projectile Motion	425	(1)
Chapter Test	426	(1)
Additional Topics in Trigonometry	427	(60)
Law of Sines	428	(9)
Law of Cosines	437	(7)
Vectors in the Plane	444	(14)
Vectors and Dot Products	458	(9)
Trigonometric Form of a Complex Number	467	(20)
Chapter Summary	478	(1)
Review Exercises	479	(4)
Chapter Project: Adding Vectors Graphically	483	(1)
Chapter Test	484	(1)
Cumulative Test: Chapters 4--6	485	(2)
Systems of Equations and Inequalities	487	(64)
Solving Systems of Equations	488	(11)
Systems of Linear Equations in Two Variables	499	(10)
Multivariable Linear Systems	509	(16)
Systems of Inequalities	525	(10)
Linear Programming	535	(16)
Chapter Summary	545	(1)
Review Exercises	546	(3)
Chapter Project: Fitting Models to Data	549	(1)
Chapter Test	550	(1)
Matrices and Determinants	551	(66)
Matrices and Systems of Equations	552	(15)
Operations with Matrices	567	(15)
The Inverse of a Square Matrix	582	(9)
The Determinant of a Square Matrix	591	(8)
Applications of Matrices and Determinants	599	(18)
Chapter Summary	609	(1)
Review Exercises	610	(5)
Chapter Project: Solving Systems of Equations	615	(1)
Chapter Test	616	(1)
Sequences, Series, and Probability	617	(78)
Sequences and Series	618	(11)
Arithmetic Sequences and Partial Sums	629	(9)
Geometric Sequences and Series	638	(10)
Mathematical Induction	648	(8)
The Binomial Theorem	656	(8)
Counting Principles	664	(10)
Probability	674	(21)
Chapter Summary	687	(1)
Review Exercises	688	(5)
Chapter Project: Fitting Models to Data	693	(1)
Chapter Test	694	(1)
Topics in Analytic Geometry	695	(74)
Introduction to Conics: Parabolas	696	(8)
Ellipses	704	(9)
Hyperbolas	713	(9)
Rotation and Systems of Quadratic Equations	722	(9)
Parametric Equations	731	(8)
Polar Coordinates	739	(6)
Graphs of Polar Equations	745	(9)
Polar Equations of Conics	754	(15)
Chapter Summary	760	(1)
Review Exercises	761	(4)
Chapter Project: Polar, Rectangular, and Parametric Forms	765	(1)
Chapter Test	766	(1)
Cumulative Test: Chapters 7--10	767	(2)
Analytic Geometry in Three Dimensions	769	(36)
The Three-Dimensional Coordinate System	770	(7)
Vectors in Space	777	(7)
The Cross Product of Two Vectors	784	(7)
Lines and Planes in Space	791	(14)
Chapter Summary	800	(1)
Review Exercises	801	(2)
Chapter Project: Distance Between a Point and a Line	803	(1)
Chapter Test	804	(1)
Limits and an Introduction to Calculus	805	(1)
Introduction to Limits	806	(10)
Techniques for Evaluating Limits	816	(10)
The Tangent Line Problem	826	(9)
Limits at Infinity and Limits of Sequences	835	(8)
The Area Problem	843	(8)
Chapter Summary	851	(1)
Review Exercises	852	(3)
Chapter Project: Tangent Lines to Sine Curves	855	(1)
Chapter Test	856	(1)
Cumulative Test: Chapters 11--12	857	(1)
Appendices
Appendix A Proofs of Selected Theorems	A1
Appendix B Concepts in Statistics	A15
B.1 Representing Data	A15
B.2 Measures of Central Tendency and Dispersion	A22
B.3 Least Squares Regression	A31
Appendix C Solving Linear Equations and Inequalities	A33
Answers to Odd-Numbered Exercises and Tests	A39
Index of Applications	A181
Index	A184