Finite Mathematics and Calculus with Applications

Margaret Lial / Raymond N. Greenwell / Nathan P. Ritchey  
Total pages
November 2013
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Finite Mathematics and Calculus with Applications, Ninth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as “Your Turn” exercises and “Apply It” vignettes that encourage active participation. The MyMathLab® course for the text provides additional learning resources for students, such as video tutorials, algebra help, step-by-step examples, and graphing calculator help. The course also features many more assignable exercises than the previous edition.


  • A wide variety of applications reference real data from articles in newspapers, journals, and websites. Examples with recent data help students learn how the mathematics is applied to their field of study, immediately addressing the question “why are we learning this?”
    • Apply It opens most sections with a provocative, real-world oriented question that is addressed in the exposition and exercises.
    • Applied exercises are grouped by type of application and highlighted for easy identification.
    • Extended Applications appear at the end of all chapters to stimulate student interest and foster in-depth learning. Directions forGroup Projects in the Extended Applications provide an opportunity for cooperative learning.
    • Index of Applications provides instructors and students with an overview of the types of applications throughout the book.
    • NEW! Application exercises within MyMathLab are now labeled by type of application.
  • Assessment and remediation features appear at key points to ensure that students keep up with the material, and provide plenty of pointers to help those who fall behind.
    • NEW! “Your Turn” exercises following selected examples provide students with an easy way to stop and check their understanding of the skill or concept being presented. Answers are provided at the end of the section’s exercises.
    • NEW! The Prerequisite Skills Diagnostic Test, just prior to Chapter R, gives students and instructors an opportunity to assess students’ skills on topics that are critical to success in this course. Answers reference specific review material in the text for targeted remediation.
    • Algebra Reference chapter appears at the beginning of the text, allowing students to brush up on their algebra skills.
    • “For Review” boxes in the margin provide immediate review, or refer students back to appropriate sections as needed.
    • Chapter Summaries include important concepts, rules, and formulas, helping students review what they have learned.
    • Caution boxes warn students of common errors/misconceptions and Note boxes offer additional useful information. Both are highlighted for easy reference.
  • Diverse exercise sets show how math is used in students’ major courses of study—business, life science, and social sciences.
    • Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
    • Writing Exercises, denoted with an icon, provide students with an opportunity to write about important mathematical ideas.
    • Technology Exercises, denoted with an icon, explore concepts using a graphing calculator or spreadsheet.
    • Concept Check exercises in the Chapter reviews help students verify their understanding of important topics.
    • NEW! Reference Tables for Exercises appear in the back of the book, next to the answers to odd-numbered exercises. These tables correlate homework exercises to a helpful example in the text.
  • Technology coverage keeps your classroom and students up-to-date with the latest software and technology options available on the market.
    • NEW! The updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.
    • Excel®Spreadsheets are included in examples and exercises where appropriate, allowing students to work problems that closely relate to real-life and business situations.
    • Graphing Calculator discussions are included in many examples, but are not essential for understanding the text. Figures depicting graphing calculator screens now feature the new TI MathPrint™ operating system.
  • MyMathLab® provides a complete online course designed to increase student achievement. The course contains over 4,100 assignable exercises with help features that can be customized to the needs of your course. It also features video tutorials, algebra diagnostic and remediation, and more.


New to this Edition

  • Based on the authors’ experience in the classroom along with feedback from many instructors across the country, this revision improves the clarity of the presentation and provides students with more opportunities to learn, practice, and apply what they’ve learned on their own.
  • The Prerequisite Skills Diagnostic Test gives students and instructors a means to assess the basic prerequisite skills needed to be successful in this course. Answers to the test include references to specific content in the algebra review chapter. The solutions to the questions are included in an appendix so students can self-remediate in a targeted fashion.
  • More applications and exercises include real data.
  • The Instructor’s Edition (AIE) is nowfully annotated. It includes valuable teaching tips in the margins for those instructors who are new to teaching this course. In addition, answers to most exercises are provided directly on the exercise set page to make it easier to assign and check homework. Challenging exercises are labeled with a plus sign (“+”) in the AIE to make them easy to identify.
  • New to the MyMathLab course
    • A “Getting Ready for Applied Calculus” chapter covers prerequisite skills. Used together with the pre-made Diagnostic Tests and Personalized Homework feature, MyMathLab provides a realistic way to address gaps in basic algebra skills.
    • Personalized Homework functionality allows instructors to create homework assignments based on the results of student assessments
    • Tutorial videos for every section of the textbook cover important concepts and terms, and are easily accessible for students who miss lecture.
    • Application labels within exercise sets (e.g., “Business/Econ”) make it easy for instructors to find types of applications appropriate to students.
    • A Ready-To-Go MyMathLab course option for this book provides students with all the same great MyMathLab features that you’re used to, but make it easier for instructors to get started. Each course includes pre-assigned homeworks and quizzes to make creating your course even simpler. For this book, the Ready-to-Go option includes:
      • Prerequisite Skills Test with accompanying personalized homework for remediation
      • A homework assignment for each section of the book
      • Chapter Review Self-Check Quiz with accompanying personalized homework
    • Interactive Figures designed for both in-class teaching and independent learning. Make them a part of assignments with Interactive Figure Questions in MyMathLab.
  • Enhanced examples include more detailed annotations to guide students through new concepts and skills. Since students tend to refer back to the examples for help with homework, they will find this new feature especially helpful.
  • “Your Turn” exercises, following selected examples, provide students with an easy way to stop and check their understanding of the skill or concept being presented. Answers are provided at the end of the section’s exercises.
  • Tailor your technology coverage—material on graphing calculators or Excel® is now set off to make it easier for students and instructors to find if they want to use this technology, or to skip if they don't.
    • All of the figures depicting graphing calculator screens have been redrawn to create a more accurate depiction of the math.
    • This edition references and provides students with a transition to the new MathPrint™ operating system of the TI-84 Plus through the technology notes, a new appendix, and the Graphing Calculator and Excel Spreadsheet Manual.
  • New and updated Extended Applications include new problems and new data sets based on current, relevant sources.
  • Reference Tables for Exercises appear in the back of the book, next to the answers to odd-numbered exercises. These tables correlate exercises to a specific example in the text; for review exercises, they refer to the section in the chapter where the topic of the exercise is first discussed.



Content Updates

  • More than 20% of the applications and 32% of the examples are new or updated. In addition, the authors have added or updated more than 600 exercises.
  • Chapter R (Algebra Reference): The flow of the material was improved through the reordering of some exercises and examples. Exercises were added to section R.1 (on performing algebraic operations) and section R.5 (on solving inequalities).
  • Chapter 1 (Linear Functions): Changes in the presentation were made throughout to increase clarity, including adding some examples and rewriting others. Terminology in Section 1.2 (Linear Functions and Applications) was adjusted to be more consistent with usage in economics.
  • Chapter 2 (Systems of Linear Equations and Matrices): Section 2.1 (Solution of Linear Systems by the Echelon Method) was changed so that only systems of two equations are solved by the echelon method, while systems with three or more equations are postponed until the Gauss-Jordan method in Section 2.2 (Solution of Linear Systems by the Gauss-Jordan Method). The discussion of subtraction of matrices in Section 2.3 was simplified.
  • Chapter 3 (Linear Programming: The Graphical Method): The concept of bounded and unbounded regions was moved from Section 3.2 (Solving Linear Programming Problems Graphically) to Section 3.1 (Graphing Linear Inequalities), where such regions are first encountered. An Extended Application on sensitivity analysis was added to this chapter.
  • Chapter 4 (Linear Programming: The Simplex Method): Exercises 25–30 in Section 4.1 (Slack Variables and the Pivot) were modified to clarify the role of slack variables. Exercise 30 in Section 4.2 was modified to amplify how multiple solutions may arise. The method for handling ties in nonstandard problems in Section 4.4 (Nonstandard Problems) was improved.
  • Chapter 5 (Mathematics of Finance): In Section 5.1 (Simple and Compound Interest), examples and accompanying exercises were added covering how to solve for the interest rate and how to find the compounding time, both with a graphing calculator and with logarithms. The explanation of the rule of 70 and the rule of 72 was improved. Material on continuous compounding was also added to Section 5.1. In Section 5.3 (Present Value of an Annuity; Amortization) an example and accompanying exercises were added discussing how a loan can be paid off early.
  • Chapter 6 (Logic): Many exercises in this chapter were revised so that the information would be more relevant to students. For example, tax references include scholarships, tuition, paychecks, reporting tips, filing taxes, inheritances, and tuition deductions; law references include car accidents, contracts, lawsuits, driver’s license, and marriage; and warranty references cover the iPhone™ and eBay®. In Section 6.5 (Analyzing Arguments and Proofs), applications were revised to give more diversity in topics.
  • Chapter 7 (Sets and Probability): Empirical probability was moved from Section 7.4 (Basic Concepts of Probability) to 7.3 (Introduction to Probability) so that methods for determining probability are contained in the same section. In Section 7.4, probability distributions are emphasized more and a probability distribution example was added. In Section 7.6 (Bayes’ Theorem) the introduction to Bayes’ Theorem was rewritten for brevity and clarity.
  • Chapter 8 (Counting Principles; Further Probability Topics): The notation for combinations was changed from (nr) to C(n, r) to be more current and consistent with our notation throughout the book. Section 8.3 (Probability Applications of Counting Principles) now includes an example illustrating probabilities using permutations and using the multiplication principle.
  • Chapter 9 (Statistics): In Section 9.1 (Frequency Distributions; Measures of Central Tendency) a new example was added, illustrating a case where the median is a truer representation of data than the mean.
  • Chapter 10 (Nonlinear Functions): The material in Section 10.1 (Properties of Functions) on the Dow Jones Average was updated. Material on even and odd functions was added. Material on identifying the degree of a polynomial has been rewritten as an example to better highlight the concept. The discussion of the Rule of 70 and the Rule of 72 was improved. A new Extended Application on Power Functions has been added.
  • Chapter 11 (The Derivative): In Section 11.1 (Limits), the introduction of limits was completely revised. The opening discussion and example were transformed into a series of examples that progress through different limit scenarios: a function defined at the limit, a function undefined at the limit (a hole in the graph), a function defined at the limit but with a different value than the limit (a piecewise function), and then finally, finding a limit when one does not exist. New figures were added to illustrate the different scenarios. In Section 11.2 (Continuity) the definition and example of continuity has been revised using a simple process to test for continuity. The opening discussion of Section 11.5 (Graphical Differentiation) showing how to sketch the graph of the derivative given the graph of the original function was rewritten as an example.
  • Chapter 12 (Calculating the Derivative): The introduction to the chain rule was rewritten as an example in Section 12.3 (The Chain Rule). Exercise topics were revised to cover subjects such as worldwide Internet users, online learning, and the Gateway arch.
  • Chapter 13 (Graphs and the Derivative): In Section 13.1 (Increasing and Decreasing Functions) the definition of increasing/decreasing functions has been moved to the beginning of the chapter, followed by the discussion of using derivatives to determine where the function increases and decreases. The determination of where a function is increasing or decreasing is divided into three examples: when the critical numbers are found by setting the derivative equal to zero, when the critical numbers are found by determining where the derivative is undefined, and when the function has no critical numbers.
  • Chapter 14 (Applications of the Derivative): Changes in the presentation were made throughout to increase clarity and exercise sets were rearranged to improve progression and parity.
  • Chapter 15 (Integration): The social sciences category of exercises was added to Section 15.1 (Antiderivatives), including the topics of bachelor's degrees and the number of females earning degrees in dentistry. Color was added to the introduction and first example of substitution in Section 15.2 (Substitution) to enable students to follow the substitution more easily.
  • Chapter 16 (Further Techniques and Applications of Integration): In addition to exercises based on real data being updated, examples in this chapter were changed for pedagogical reasons.
  • Chapter 17 (Multivariable Calculus): Graphs generated by Maple™ were added to Examples 2 and 4 in Section 17.3 (Maxima and Minima) to assist students in visualizing the concept of relative extrema. Material covering utility functions was added to Section 17.4.
  • Chapter 18 (Probability and Calculus): In Section 18.2 (Expected Value and Variance of Continuous Random Variables), an example on how to calculate the probability within one standard deviation of the mean (which is required in many of the exercises) was added. The Social Sciences category was added to the exercise set, with exercises on calculating the median, expected value, and standard deviation. Topics include the time it takes to learn a task and the age of users of a social network.


Table of Contents

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals


1. Linear Functions

1.1 Slopes and Equations of Lines

1.2 Linear Functions and Applications

1.3 The Least Squares Line

Chapter 1 Review

Extended Application: Using Extrapolation to Predict Life Expectancy


2. Systems of Linear Equations and Matrices

2.1 Solution of Linear Systems by the Echelon Method

2.2 Solution of Linear Systems by the Gauss-Jordan Method

2.3 Addition and Subtraction of Matrices

2.4 Multiplication of Matrices

2.5 Matrix Inverses

2.6 Input-Output Models

Chapter 2 Review

Extended Application: Contagion


3. Linear Programming: The Graphical Method

3.1 Graphing Linear Inequalities

3.2 Solving Linear Programming Problems Graphically

3.3 Applications of Linear Programming

Chapter 3 Review

Extended Application: Sensitivity Analysis


4. Linear Programming: The Simplex Method

4.1 Slack Variables and the Pivot

4.2 Maximization Problems

4.3 Minimization Problems; Duality

4.4 Nonstandard Problems

Chapter 4 Review

Extended Application: Using Integer Programming in the Stock-Cutting Problem


5. Mathematics of Finance

5.1 Simple and Compound Interest

5.2 Future Value of an Annuity

5.3 Present Value of an Annuity; Amortization

Chapter 5 Review

Extended Application: Time, Money, and Polynomials


6. Logic

6.1 Statements

6.2 Truth Tables and Equivalent Statements

6.3 The Conditional and Circuits

6.4 More on the Conditional

6.5 Analyzing Arguments and Proofs

6.6 Analyzing Arguments with Quantifiers

Chapter 6 Review

Extended Application: Logic Puzzles


7. Sets and Probability

7.1 Sets

7.2 Applications of Venn Diagrams

7.3 Introduction to Probability

7.4 Basic Concepts of Probability

7.5 Conditional Probability; Independent Events

7.6 Bayes' Theorem

Chapter 7 Review

Extended Application: Medical Diagnosis


8. Counting Principles; Further Probability Topics

8.1 The Multiplication Principle; Permutations

8.2 Combinations

8.3 Probability Applications of Counting Principles

8.4 Binomial Probability

8.5 Probability Distributions; Expected Value

Chapter 8 Review

Extended Application: Optimal Inventory for a Service Truck


9. Statistics

9.1 Frequency Distributions; Measures of Central Tendency

9.2 Measures of Variation

9.3 The Normal Distribution

9.4 Normal Approximation to the Binomial Distribution

Chapter 9 Review

Extended Application: Statistics in the Law - The Castaneda Decision


10. Nonlinear Functions

10.1 Properties of Functions

10.2 Quadratic Functions; Translation and Reflection

10.3 Polynomial and Rational Functions

10.4 Exponential Functions

10.5 Logarithmic Functions

10.6 Applications: Growth and Decay; Mathematics of Finance

Chapter 10 Review

Extended Application: Characteristics of the Monkeyface Prickleback


11. The Derivative

11.1 Limits

11.2 Continuity

11.3 Rates of Change

11.4 Definition of the Derivative

11.5 Graphical Differentiation

Chapter 11 Review

Extended Application: A Model for Drugs Administered Intravenously


12. Calculating the Derivative

12.1 Techniques for Finding Derivatives

12.2 Derivatives of Products and Quotients

12.3 The Chain Rule

12.4 Derivatives of Exponential Functions

12.5 Derivatives of Logarithmic Functions

Chapter 12 Review

Extended Application: Electrical Potential and Electric Field


13. Graphs and the Derivative

13.1 Increasing and Decreasing Functions

13.2 Relative Extrema

13.3 Higher Derivatives, Concavity, and the Second Derivative Test

13.4 Curve Sketching

Chapter 13 Review

Extended Application: A Drug Concentration Model for Orally Administered Medications


14. Applications of the Derivative

14.1 Absolute Extrema

14.2 Applications of Extrema

14.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand

14.4 Implicit Differentiation

14.5 Related Rates

14.6 Differentials: Linear Approximation

Chapter 14 Review

Extended Application: A Total Cost Model for a Training Program


15. Integration

15.1 Antiderivatives

15.2 Substitution

15.3 Area and the Definite Integral

15.4 The Fundamental Theorem of Calculus

15.5 The Area Between Two Curves

15.6 Numerical Integration

Chapter15 Review

Extended Application: Estimating Depletion Dates for Minerals


16. Further Techniques and Applications of Integration

16.1 Integraton by Parts

16.2 Volume and Average Value

16.3 Continuous Money Flow

16.4 Improper Integrals

Chapter 16 Review

Extended Application: Estimating Learning Curves in Manufacturing with Integrals


17. Multivariable Calculus

17.1 Functions of Several Variables

17.2 Partial Derivatives

17.3 Maxima and Minima

17.4 Lagrange Multipliers

17.5 Total Differentials and Approximations

17.6 Double Integrals

Chapter 17 Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design


18. Probability and Calculus

18.1 Continuous Probability Models

18.2 Expected Value and Variance of Continuous Random Variables

18.3 Special Probability Density Functions

Chapter 18 Review

Extended Application: Exponential Waiting Times