Precalculus with Limits Book

Chapter R: Basic Algebraic Operations

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Review Exercises

Chapter R Group Activity: Rational and Irrational Numbers

Chapter 1: Equations and Inequalities

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value in Equations and Inequalities

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Additional Equation-Solving Techniques

Chapter 1 Review

Chapter 1 Review Exercises

Chapter 1 Group Activity: Solving a Cubic Equation

Chapter 2: Graphs

2-1 Cartesian Coordinate System

2-2 Distance in the Plane

2-3 Equations of a Line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Review Exercises

Chapter 2 Group Activity: Rates of Change

Chapter 3: Functions

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Operations on Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Review Exercises

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Cumulative Review Exercises Chapters 1-3

Chapter 4: Polynomials and Rational Functions

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Review Exercises

Chapter 4 Group Activity: Interpolating Polynomials

Chapter 5: Exponential and Logarithmic Functions

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Review Exercises

Chapter 5 Group Activity: Comparing Regression Models

Cumulative Review Exercises Chapters 4-5

Chapter 6: Trigonometric Functions

6-1 Angles and Their Measure

6-2 Trigonometric Functions: A Unit Circle Approach

6-3 Solving Right Triangles

6-4 Properties of Trigonometric Functions

6-5 More General Trigonometric Functions and Models

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Review Exercises

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

Chapter 7: Trigonometric Identities and Conditional Equations

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Review Exercises

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C): A Harmonic Analysis Tool

Chapter 8: Additional Topics in Trigonometry

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Review Exercises

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Cumulative Review Exercises Chapters 6-8

Chapter 9: Additional Topics in Analytic Geometry

9-1 Conic Sections; Parabolas

9-2 Ellipse

9-3 Hyperbola

9-4 Translation and Rotation of Axes

Chapter 9 Review

Chapter 9 Review Exercises

Chapter 9 Group Activity: Focal Chords

Chapter 10: Systems of Equations and Inequalities; Matrices

10-1 Systems of Linear Equations in Two Variables

10-2 Systems of Linear Equations in Three Variables

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrix Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Review Exercises

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

Chapter 11: Sequences, Induction, and Probability

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Review Exercises

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Cumulative Review Exercises Chapters 9-11

Chapter 12 Limits: An Introduction to Calculus

12-1 Introduction to Limits

12-2 Computing Limits Algebraically

12-3 Limits at Infinity

12-4 The Derivative

12-5 Area and Calculus

Chapter 12 Review

Chapter 12 Review Exercises

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

Appendix A: Special Topics
A-1 Scientific Notation and Significant Digits
A-2 Partial Fractions
A-3 Parametric Equations
Appendix B: Geometric Formulas
Student Answers
Subject Index