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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. Enhanced WebAssign® features fully integrated content from the text, with the addition of End-of-Section problems and Chapter Tests, as well as problem-specific videos, animations, and lecture videos.
- Fresh Chapter Openers highlight real-life problems that connect to the examples and exercises presented in the following chapter.
- Innovative Summarize Features help students organize the lesson's key concepts into a concise summary, providing a valuable study tool at the end of each section.
- Unprecedented How Do You See It? Exercises in every section present real-life problems that students solve by visual inspection using the concepts in the lesson.
- Original Checkpoint Problems encourage immediate practice and check students' understanding of the concepts in the paired example.
- New Series Companion Website features chapter projects, data tables, assessments, study tools, video solutions, and more to support students outside the text.
- Enhanced Exercise Sets deliver more rigor, relevancy, and coverage than ever before and feature multi-step, real-life exercises to reinforce problem-solving skills and mastery of concepts.
- Expanded Section Objectives offer students the opportunity to preview what will be presented in the upcoming section.
- Enriched Remarks reinforce or expand on concepts helping students learn how to study mathematics, avoid common errors, address special cases, or show alternative or additional steps to a solution of an example.
- Up-to-the-minute homework support through CalcChat.com, an independent website, provides students with free solutions to all odd-numbered problems in the text.
- Side-By-Side Examples help students see not only that a problem can be solved in more than one way but also how different methods--algebraically, graphically, and numerically--yield the same result. The side-by-side format also addresses many different learning styles.
- Algebra Helps direct students to sections of the textbook where they can review algebra skills needed to master the current topic.
- Technology Features offer suggestions for effectively using tools such as calculators, graphing calculators, and spreadsheet programs to deepen student understanding of concepts, ease lengthy calculations, and provide alternate solution methods for verifying answers obtained by hand.
- Historical Notes provide helpful information regarding basic mathematical foundations.
- Algebra of Calculus Examples and Exercises throughout the text emphasize various algebraic techniques used in calculus.
- Vocabulary Exercises at the beginning of the exercise set for each section help students review previously learned vocabulary terms necessary to solve the section exercises.
- Student Projects in various sections and online feature in-depth applied exercises with large, real-life data sets, where students create or analyze models.
- Chapter Summaries include explanations and examples of the objectives taught in the chapter.
- Larson PRECALCULUS WITH LIMITS is ideal for a two-term course.
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.
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.
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.
Concepts in Statistics (web).
B.1 Representing Data.
B.2 Measures of Central Tendency and Dispersion.
B.3 Least Squares Regression.
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.
Online Test Bank
Simplify testing and assessment using this printed selection of questions.
Complete Solutions Manual
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
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
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
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
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.
Student Study Guide and Solutions Manual
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
This innovative study aid, in the form of a notebook organizer, helps you develop a section-by-section summary of key concepts.