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Overview

With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS covers analytic geometry in three dimensions and introduces concepts covered in calculus.

Ron Larson, The Pennsylvania State University, The Behrend College

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the bestselling Calculus series published by Cengage.
  • NEW Cap Stone Exercises - the Cap Stone exercises assesses students understanding of all concepts covered in the section's material.
  • NEW detailed Chapter Review - The new edition now includes explanations and/or examples for all learning objectives. This will further promote students' understanding of the material.
  • NEW Caution/Warning boxes - The warnings cautions students away from common errors and pitfalls.
  • NEW Algebra Helps - the author provides appropriate caution boxes, study tips and algebra helps to guide the student through difficult concepts.
  • Improved Examples (graphical solution side by side with algebraic solution). This is intended to improve the students graphical understanding of algebra.
  • New/Revised End of section exercises.
  • Enhanced WebAssign.
  • Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts.
  • Exercise Sets have been carefully analyzed and revised to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications.
  • Side-by-side Example Solutions for select examples include multiple problem solving approaches—such as algebraic, graphical, and numerical—to appeal to a variety of teaching and learning styles.
  • Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, allowing students to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book.
1. FUNCTIONS AND THEIR GRAPHS.
Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving.
4. TRIGONOMETRY.
Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
5. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
6. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving.
7. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
8. MATRICES AND DETERMINANTS.
Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
9. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving.
10. TOPICS IN ANALYTIC GEOMETRY.
Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
11. ANALYTIC GEOMETRY IN THREE DIMENSIONS.
The Three-Dimensional Coordinate System. Vectors in Space. The Cross Product of Two Vectors. Lines and Planes in Space. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving.
12. LIMITS AND AN INTRODUCTION TO CALCULUS.
Introduction to Limits. Techniques for Evaluating Limits. The Tangent Line Problem. Limits at Infinity and Limits of Sequences. The Area Problem. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 10-12. Proofs in Mathematics. P.S. Problem Solving.
APPENDIX A: REVIEW OF FUNDAMENTAL CONCEPTS OF ALGEBRA.
Real Numbers and Their Properties. Exponents and Radicals. Polynomials and Factoring. Rational Expressions. Solving Equations. Linear Inequalities in One Variable. Errors and the Algebra of Calculus.
APPENDIX B: CONCEPTS IN STATISTICS (WEB).
Representing Data. Measures of Central Tendency and Dispersion. Least Squares Regression.
WebAssign
Each WebAssign online product offers the full textbook combined with a flexible and fully customizable online instructional assignments and tools.

Cengage provides a seamless user experience for Learning Management Systems (LMS) integration. Please contact your Cengage Learning Consultant for ordering information and visit our Learning Management System Integration web page on WebAssign for general information.

Standalone Digital Access — Ultimate Value

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Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

FOR INSTRUCTORS

Online Test Bank

ISBN: 9781337279659
Simplify testing and assessment using this printed selection of questions.

Complete Solutions Manual

ISBN: 9781337279413
This time-saving manual provides complete solutions to all the exercises from the text, including Chapter Review Exercises and Chapter Tests.

Instructor's Website with PowerPoint®, Image Library Slides

ISBN: 9781337279406
Microsoft® PowerPoint® slides and image library for the entire book, posted on the Instructor Companion Website, let you incorporate images from the book right into your lectures.

Cengage Learning Testing, powered by Cognero® Instant Access

ISBN: 9781337279390
Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to: import, edit, and manipulate content from the text's test bank or elsewhere, including your own favorite test questions; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want. This is available online via www.cengage.com/login.

Student Study Guide and Solutions Manual

ISBN: 9781337279185
This guide offers step-by-step solutions for all odd-numbered text exercises, Chapter and Cumulative Tests, and Practice Tests with solutions, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

Note Taking Guide

ISBN: 9781337279291
This is an innovative study aid, in the form of a notebook organizer which helps students develop a section-by-section summary of key concepts.

FOR STUDENTS

Student Study Guide and Solutions Manual

ISBN: 9781337279185
This guide offers step-by-step solutions for all odd-numbered text exercises, Chapter and Cumulative Tests, and Practice Tests with solutions, giving you a way to check your answers.

Note Taking Guide

ISBN: 9781337279291
This innovative study aid, in the form of a notebook organizer, helps you develop a section-by-section summary of key concepts.