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Precalculus with Calculus Previews, 5th Edition

Book Description

Incorporating Zill's student-friendly writing style and modern examples, Precalculus with Calculus Previews, Fifth Edition includes all of the outstanding features and learning tools found in the original text, Essentials of Precalculus with Calculus Previews, while incorporating additional coverage that some courses may require. With a continued aim to keep the text complete, yet concise, the authors added four additional chapters making the text a clear choice for many mainstream courses. This student-friendly, four-color text offers numerous exercise sets and examples to aid in students' learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. - Includes a new chapter, - Provides a "no nonsense" approach to precalculus with an informal, intuitive, and straightforward writing style. - Incorporates the terminology used in calculus in an informal way to acclimate students to these new terms. - Includes over 1600 figures to help illuminate key concepts. - Notes from the Classroom sections address a variety of student/textbook/classroom/calculus issues such as alternative terminology, reinforcement of important concepts, tips on memorization, misinterpretations, common errors, solution procedures, calculators, and advice on the importance of neatness and organization. - Calculus Previews conclude each chapter and highlight a single calculus concept with a focus on the algebraic, logarithmic, and trigonometric manipulations necessary for successfully completing the problem. Translating Words into Functions illustrates how to translate a verbal description into a symbolic representation of a function.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. 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 Calculus Preview: Algebra and Limits
    6. Chapter 1 Review Exercises
  7. 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 Inverse Functions
    8. 2.8 Building a Function from Words
    9. 2.9 Calculus Preview: The Tangent Line Problem
    10. Chapter 2 Review Exercises
  8. 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 Calculus Preview: The Area Problem
    8. Chapter 3 Review Exercises
  9. 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 Calculus Preview: The Limit Concept Revisited
    12. Chapter 4 Review Exercises
  10. 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 Calculus Preview: Vectors and Dot Product
    6. Chapter 5 Review Exercises
  11. 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 Calculus Preview: The Hyperbolic Functions
    6. Chapter 6 Review Exercises
  12. 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 Calculus Preview: 3-Space
    6. Chapter 7 Review Exercises
  13. 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 Calculus Preview: Parametric Equations
    5. Chapter 8 Review Exercises
  14. 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 Calculus Preview: Partial Fractions
    6. Chapter 9 Review Exercises
  15. 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 Calculus Preview: Convergence of Sequences and Series
    8. Chapter 10 Review Exercises
  16. Final Examination
  17. Apppendix A: Complex Numbers
  18. Apppendix B: Descartes’ Rule of Signs
  19. Apppendix C: Formulas from Geometry
  20. Answers to Selected Odd-Numbered Problems
  21. Index
  22. Credits