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Precalculus with Calculus Previews, 6th Edition

Book Description

Building off the success of Zill and Dewar's popular Essentials version, the new Sixth Edition of Precalculus with Calculus Previews continues to include all of the outstanding features and learning tools found in the original text while incorporating additional topics of coverage that some courses may require. With a continued effort to keep the text complete, yet concise, the authors have included four additional chapters making the text a clear choice for many mainstream courses. Additional chapters include a new chapter on Polar Coordinates, as well as Triangle Trigonometry, Systems of Equations and Inequalities, and Sequences and Series.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1 Inequalities, Equations, and Graphs
    1. 1.1 The Real Line
    2. 1.2 Absolute Value
    3. 1.3 The Rectangular Coordinate System
    4. 1.4 Circles and Graphs
    5. 1.5 Algebra and Limits
    6. Chapter 1 Review Exercises
  7. Chapter 2 Functions
    1. 2.1 Functions and Graphs
    2. 2.2 Symmetry and Transformations
    3. 2.3 Linear Functions
    4. 2.4 Quadratic Functions
    5. 2.5 Piecewise-Defined Functions
    6. 2.6 Combining Functions
    7. 2.7 Functions Defined Implicitly
    8. 2.8 Inverse Functions
    9. 2.9 Building a Function from Words
    10. 2.10 The Tangent Line Problem
    11. Chapter 2 Review Exercises
  8. Chapter 3 Polynomial and Rational Functions
    1. 3.1 Polynomial Functions
    2. 3.2 Division of Polynomial Functions
    3. 3.3 Zeros and Factors of Polynomial Functions
    4. 3.4 Real Zeros of Polynomial Functions
    5. 3.5 Approximating Real Zeros
    6. 3.6 Rational Functions
    7. 3.7 The Area Problem
    8. Chapter 3 Review Exercises
  9. Chapter 4 Trigonometric Functions
    1. 4.1 Angles and Their Measurement
    2. 4.2 The Sine and Cosine Functions
    3. 4.3 Graphs of Sine and Cosine Functions
    4. 4.4 Other Trigonometric Functions
    5. 4.5 Verifying Trigonometric Identities
    6. 4.6 Sum and Difference Formulas
    7. 4.7 Product-to-Sum and Sum-to-Product Formulas
    8. 4.8 Inverse Trigonometric Functions
    9. 4.9 Trigonometric Equations
    10. 4.10 Simple Harmonic Motion
    11. 4.11 The Limit Concept Revisited
    12. Chapter 4 Review Exercises
  10. Chapter 5 Triangle Trigonometry
    1. 5.1 Right Triangle Trigonometry
    2. 5.2 Applications of Right Triangles
    3. 5.3 Law of Sines
    4. 5.4 Law of Cosines
    5. 5.5 Vectors and Dot Product
    6. Chapter 5 Review Exercises
  11. Chapter 6 Exponential and Logarithmic Functions
    1. 6.1 Exponential Functions
    2. 6.2 Logarithmic Functions
    3. 6.3 Exponential and Logarithmic Equations
    4. 6.4 Exponential and Logarithmic Models
    5. 6.5 The Hyperbolic Functions
    6. Chapter 6 Review Exercises
  12. Chapter 7 Conic Sections
    1. 7.1 The Parabola
    2. 7.2 The Ellipse
    3. 7.3 The Hyperbola
    4. 7.4 Rotation of Axes
    5. 7.5 3-Space
    6. Chapter 7 Review Exercises
  13. Chapter 8 Polar Coordinates
    1. 8.1 The Polar Coordinate System
    2. 8.2 Graphs of Polar Equations
    3. 8.3 Conic Sections in Polar Coordinates
    4. 8.4 Parametric Equations
    5. Chapter 8 Review Exercises
  14. Chapter 9 Systems of Equations and Inequalities
    1. 9.1 Systems of Linear Equations
    2. 9.2 Determinants and Cramer’s Rule
    3. 9.3 Systems of Nonlinear Equations
    4. 9.4 Systems of Inequalities
    5. 9.5 Partial Fractions
    6. Chapter 9 Review Exercises
  15. Chapter 10 Sequences and Series
    1. 10.1 Sequences
    2. 10.2 Series
    3. 10.3 Mathematical Induction
    4. 10.4 The Binomial Theorem
    5. 10.5 Principles of Counting
    6. 10.6 Introduction to Probability
    7. 10.7 Convergence of Sequences and Series
    8. Chapter 10 Review Exercises
  16. Final Examination
  17. Appendixes
    1. A. Complex Numbers
      1. A.1 Arithmetic Operations and Properties
      2. A.2 Trigonometric Form of Complex Numbers
      3. A.3 Powers and Roots of Complex Numbers
    2. B. Additional Tests for Zeros of a Polynomial Function
      1. B.1 Descartes’ Rule of Signs
      2. B.2 Upper and Lower Bounds Rule
    3. C. Formulas From Geometry
  18. Answers to Selected Odd-Numbered Problems
  19. Index