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Larson's PRECALCULUS WITH LIMITS is known for delivering the same sound, consistently structured explanations and exercises of mathematical concepts as the market-leading PRECALCULUS, Ninth Edition, with a laser focus on preparing students for calculus. In LIMITS, the author includes a brief algebra review to the core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus. With the third edition, Larson continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.

"Some students in my precalculus class are very weak in algebra. . . . The 'Algebra Help' is definitely beneficial to students . . . [as are the] 'Warning/Cautions' which help those students avoid common mistakes that others make. [And] the 'Student Tips' really guide students in what they should recognize after an example is presented. . . . Larson's text is among the best precalculus books [I've found]."

"The text breaks down the material into manageable piecesâ€”I was able to cover approximately one section per lecture and assign homework after each lecture. I especially like the 'Why you should learn it' feature at the start of each section. This helped me motivate the students at the start of every lecture."

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 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, 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 best-selling Calculus series published by Cengage Learning.

1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent 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 for 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 for 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 for 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 for Chapters. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (web). B.1 Representing Data. B.2 Measures of Central Tendency and Dispersion. B.3 Least Squares Regression.

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## More About This Textbook

## Overview

Larson's PRECALCULUS WITH LIMITS is known for delivering the same sound, consistently structured explanations and exercises of mathematical concepts as the market-leading PRECALCULUS, Ninth Edition, with a laser focus on preparing students for calculus. In LIMITS, the author includes a brief algebra review to the core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus. With the third edition, Larson continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.

## Editorial Reviews

## From the Publisher

"Some students in my precalculus class are very weak in algebra. . . . The 'Algebra Help' is definitely beneficial to students . . . [as are the] 'Warning/Cautions' which help those students avoid common mistakes that others make. [And] the 'Student Tips' really guide students in what they should recognize after an example is presented. . . . Larson's text is among the best precalculus books [I've found].""The text breaks down the material into manageable piecesâ€”I was able to cover approximately one section per lecture and assign homework after each lecture. I especially like the 'Why you should learn it' feature at the start of each section. This helped me motivate the students at the start of every lecture."

## Product Details

## Related Subjects

## Meet the Author

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 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, 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 best-selling Calculus series published by Cengage Learning.

## Table of Contents

1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent 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 for 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 for 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 for 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 for Chapters. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (web). B.1 Representing Data. B.2 Measures of Central Tendency and Dispersion. B.3 Least Squares Regression.