Precalculus with Limits, Advanced

Precalculus with Limits, Advanced Precalculus with Limits, Advanced

ISBN: 9780618660902 / 0618660909

Table of Contents

Chapter 1

Functions And Their Graphs

1.1 Rectangular Coordinates Exercises p.9
1.2 Graphs of Equations Exercises p.22
1.3 Linear Equations in Two Variables Exercises p.34
1.4 Functions Exercises p.48
1.5 Analyzing Graphs of Functions Exercises p.61
1.6 A Library of Parent Functions Exercises p.71
1.7 Transformations of Functions Exercises p.79
1.8 Combinations of Functions Exercises p.89
1.9 Inverse Functions Exercises p.99
1.10 Mathematical Modeling and Variation Exercises p.109
Review Exercises p.117
Chapter 1 Test p.123
Problem Solving p.125

Chapter 2

Polynomial And Rational Functions

2.1 Quadratic Functions and Models Exercises p.134
2.2 Polynomial Functions of Higher Degree Exercises p.148
2.3 Polynomial and Synthetic Division Exercises p.159
2.4 Complex Numbers Exercises p.167
2.5 Zeros of Polynomial Functions Exercises p.179
2.6 Rational Functions Exercises p.193
Exercises p.204
Review Exercises p.208
Chapter 2 Test p.212
Problem Solving p.215

Chapter 3

Exponential And Logarithmic Functions

3.1 Exponential Functions and Their Graphs Exercises p.226
3.2 Logarithmic Functions and Their Graphs Exercises p.236
3.3 Properties of Logarithms Exercises p.243
3.4 Exponential and Logarithmic Equations Exercises p.253
3.5 Exponential and Logarithmic Models Exercises p.264
Review Exercises p.271
Chapter 3 Test p.275
Cumulative Test for Chapters 1-3 p.276
Problem Solving p.279

Chapter 4


4.1 Radian and Degree Measure Exercises p.290
4.2 Trigonometric Functions: The Unit Circle Exercises p.299
4.3 Right Triangle Trigonometry Exercises p.308
4.4 Trigonometric Functions of Any Angle Exercises p.318
4.5 Graphs of Sine and Cosine Functions Exercises p.328
4.6 Graphs of Other Trigonometric Functions Exercises p.339
4.7 Inverse Trigonometric Functions Exercises p.349
4.8 Application and Models Exercises p.359
Review Exercises p.365
Chapter 4 Test p.369
Problem Solving p.371

Chapter 5

Analytic Trigonometry

5.1 Using Fundamental Identities Exercises p.379
5.2 Verifying Trigonometric Identities Exercises p.387
5.3 Solving Trigonometric Equations Exercises p.397
5.4 Sum and Difference Formulas Exercises p.404
5.5 Multiple-Angle and Product-to-Sum Formulas Exercises p.415
Review Exercises p.420
Chapter 5 Test p.423
Problem Solving p.427

Chapter 6

Additional Topics In Trigonometry

6.1 Law of Sines Exercises p.436
6.2 Law of Cosines Exercises p.443
6.3 Vectors in the Plane Exercises p.456
6.4 Vectors and Dot Products Exercises p.467
6.5 Trigonometric Form of a Complex Number Exercises p.478
Review Exercises p.482
Chapter Test p.486
Cumulative Test for Chapters 4-6 p.487
Problem Solving p.493

Chapter 7

Systems Of Equations And Inequalities

7.1 Linear and Nonlinear Systems of Equations Exercises p.503
7.2 Two-Variable Linear Systems Exercises p.515
7.3 Multivariable Linear Systems Exercises p.527
7.4 Partial Fractions Exercises p.539
7.5 Systems of Inequalities Exercises p.548
7.6 Linear Programming Exercises p.558
Review Exercises p.563
Chapter Test p.567
Problem Solving p.569

Chapter 8

Matrices And Determinants

8.1 Matrices and Systems of Equations Exercises p.582
8.2 Operations with Matrices Exercises p.597
8.3 The Inverse of a Square Matrix Exercises p.608
8.4 The Determinant of a Square Matrix Exercises p.616
8.5 Applications of Matrices and Determinants Exercises p.628
Review Exercises p.632
Chapter Test p.637
Problem Solving p.639

Chapter 9

Sequences, Series, And Probability

9.1 Sequences and Series Exercises p.649
9.2 Arithmetic Sequences and Partial Sums Exercises p.659
9.3 Geometric Sequences and Series Exercises p.669
9.4 Mathematical Induction Exercises p.681
9.5 The Binomial Theorem Exercises p.688
9.6 Counting Principles Exercises p.698
9.7 Probability Exercises p.709
Review Exercises p.715
Chapter Test p.719
Cumulative Test for Chapters 7-9 p.720
Problem Solving p.725

Chapter 10

Topics In Analytic Geometry

10.1 Lines Exercises p.732
10.2 Introduction to ConicsL Parabolas Exercises p.740
10.3 Ellipses Exercises p.750
10.4 Hyperbolas Exercises p.760
10.5 Rotation of Conics Exercises p.769
10.6 Parametric Equations Exercises p.776
10.7 Polar Coordinates Exercises p.783
10.8 Graphs of Polar Equations Exercises p.791
10.9 Polar Equations of Conics Exercises p.797
Review Exercises p.801
Chapter 10 Test p.805
Problem Solving p.809

Chapter 11

Analytic Geometry In Three Dimensions

11.1 The Three-Dimensional Coordinate System Exercises p.817
11.2 Vectors in Space Exercises p.825
11.3 The Cross Product of Two Vectors Exercises p.832
11.4 Lines and Planes and Space Exercises p.841
Review Exercises p.844
Chapter Test p.846
Problem Solving p.849

Chapter 12

Limits And An Introduction To Calculus

12.1 Introduction to Limits Exercises p.860
12.2 Techniques for Evaluating Limits Exercises p.870
12.3 The Tangent Line Problem Exercises p.880
12.4 Limits at Infinity and Limits of Sequences Exercises p.889
12.5 The Area Problem Exercises p.898
Review Exercises p.901
Chapter Test p.904
Cumulative Test for Chapters 10-12 p.905
Problem Solving p.908

Chapter A

Review Of Fundamental Concepts Of Algebra

A.1 Real Numbers and Their Properties Exercises p.A8
A.2 Exponents and Radicals Exercises p.A20
A.3 Polynomials and Factoring Exercises p.A31
A.4 Rational Expressions Exercises p.A43
A.5 Solving Equations Exercises p.A56
A.6 Linear Inequalities in One Variable Exercises p.A66
A.7 Errors and the Algebra of Calculus Exercises p.A75
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