Precalculus

by Larson, Ron; Hostetler, Robert P.

• ISBN13: 9780618052851
• ISBN10: 0618052852
• Edition: 5th
• Format: Hardcover
• Copyright: 2000-07-11
• Publisher: Brooks Cole

Summary

As the best-seller in its field, Precalculus, 5/e, offers both instructors and students a more solid, comprehensive, and flexible program than ever before. Designed for the one- or two-term precalculus course, the text opens with moderate algebra review and introduces trigonometry first with a unit circle approach and then with the right triangle.For a complete listing of features, see Larson/Hostetler, College Algebra, 5/e.

Table of Contents

A Word from the Authors (Preface)	vii
Features Highlights	x
An Introduction to Graphing Utilities	xvi
Prerequisites	1	(97)
Real Numbers	2	(10)
Exponents and Radicals	12	(13)
Polynomials and Factoring	25	(13)
Rational Expressions	38	(11)
Solving Equations	49	(13)
Solving Inequalities	62	(12)
Errors and the Algebra of Calculus	74	(7)
Graphical Representation of Data	81	(17)
Chapter Summary	91	(1)
Review Exercises	92	(4)
Chapter Project: Numerically Finding a Maximum Volume	96	(1)
Chapter Test	97	(1)
Functions and Their Graphs	98	(102)
Graphs of Equations	100	(10)
Linear Equations in Two Variables	110	(15)
Functions	125	(14)
Analyzing Graphs of Functions	139	(13)
Shifting, Reflecting, and Stretching Graphs	152	(11)
Combinations of Functions	163	(8)
Inverse Functions	171	(10)
Mathematical Modeling	181	(19)
Chapter Summary	193	(1)
Review Exercises	194	(4)
Chapter Project: A Graphical Approach to Maximization	198	(1)
Chapter Test	199	(1)
Polynomial and Rational Functions	200	(86)
Quadratic Functions	202	(11)
Polynomial Functions of Higher Degree	213	(13)
Polynomial and Synthetic Division	226	(10)
Complex Numbers	236	(7)
Zeros of Polynomial Functions	243	(15)
Rational Functions	258	(13)
Partial Fractions	271	(15)
Chapter Summary	279	(1)
Review Exercises	280	(4)
Chapter Project: Finding Points of Intersection Graphically	284	(1)
Chapter Test	285	(1)
Exponential and Logarithmic Functions	286	(64)
Exponential Functions and Their Graphs	288	(12)
Logarithmic Functions and Their Graphs	300	(11)
Properties of Logarithms	311	(6)
Exponential and Logarithmic Equations	317	(11)
Exponential and Logarithmic Models	328	(22)
Chapter Summary	341	(1)
Review Exercises	342	(4)
Chapter Project: Graphical Approach to Compound Interest	346	(1)
Chapter Test	347	(1)
Cumulative Test: Chapters 1-3	348	(2)
Trigonometry	350	(90)
Radian and Degree Measure	352	(11)
Trigonometric Functions: The Unit Circle	363	(7)
Right Triangle Trigonometry	370	(11)
Trigonometric Functions of Any Angle	381	(9)
Graphs of Sine and Cosine Functions	390	(11)
Graphs of Other Trigonometric Functions	401	(11)
Inverse Trigonometric Functions	412	(10)
Applications and Models	422	(18)
Chapter Summary	433	(1)
Review Exercises	434	(4)
Chapter Project: Analyzing a Graph	438	(1)
Chapter Test	439	(1)
Analytic Trigonometry	440	(52)
Using Fundamental Identities	442	(8)
Verifying Trigonometric Identities	450	(7)
Solving Trigonometric Equations	457	(11)
Sum and Difference Formulas	468	(7)
Multiple-Angle and Product-to-Sum Formulas	475	(17)
Chapter Summary	486	(1)
Review Exercises	487	(3)
Chapter Project: Projectile Motion	490	(1)
Chapter Test	491	(1)
Additional Topics in Trigonometry	492	(60)
Law of Sines	494	(9)
Law of Cosines	503	(8)
Vectors in the Plane	511	(13)
Vectors and Dot Products	524	(8)
Trigonometric Form of a Complex Number	532	(20)
Chapter Summary	543	(1)
Review Exercises	544	(4)
Chapter Project: Adding Vectors Graphically	548	(1)
Chapter Test	549	(1)
Cumulative Test: Chapters 4-6	550	(2)
Systems of Equations and Inequalities	552	(66)
Solving Systems of Equations	554	(11)
Two-Variable Linear Systems	565	(12)
Multivariable Linear Systems	577	(13)
Systems of Inequalities	590	(11)
Linear Programming	601	(17)
Chapter Summary	611	(1)
Review Exercises	612	(4)
Chapter Project: Fitting Models to Data	616	(1)
Chapter Test	617	(1)
Matrices and Determinants	618	(68)
Matrices and Systems of Equations	620	(15)
Operations with Matrices	635	(14)
The Inverse of a Square Matrix	649	(9)
The Determinant of a Square Matrix	658	(8)
Applications of Matrices and Determinants	666	(20)
Chapter Summary	678	(1)
Review Exercises	679	(5)
Chapter Project: Solving Systems of Equations	684	(1)
Chapter Test	685	(1)
Sequences, Series, and Probability	686	(82)
Sequences and Series	688	(11)
Arithmetic Sequences and Partial Sums	699	(9)
Geometric Sequences and Series	708	(10)
Mathematical Induction	718	(10)
The Binomial Theorem	728	(8)
Counting Principles	736	(10)
Probability	746	(22)
Chapter Summary	759	(1)
Review Exercises	760	(4)
Chapter Project: Exploring Difference Quotients	764	(1)
Chapter Test	765	(1)
Cumulative Test: Chapters 7-9	766	(2)
Topics in Analytic Geometry	768
Lines	770	(7)
Introduction to Conics: Parabolas	777	(9)
Ellipses	786	(9)
Hyperbolas	795	(9)
Rotation of Conics	804	(8)
Parametric Equations	812	(8)
Polar Coordinates	820	(6)
Graphs of Polar Equations	826	(8)
Polar Equations of Conics	834
Chapter Summary	841	(1)
Review Exercises	842	(4)
Chapter Project: Polar, Rectangular, and Parametric Forms	846	(1)
Chapter Test	847
Appendices
Appendix A Proofs of Selected Theorems	A1
Appendix B Concepts in Statistics	A16
B.1 Representing Data	A16
B.2 Measures of Central Tendency and Dispersion	A20
B.3 Least Squares Regression	A29
Answers to Odd-Numbered Exercises and Tests	A33
Index of Applications	A155
Index	A159