Prepare for success in precalculus as Larson's PRECALCULUS WITH LIMITS, 5th Edition provides specially developed ongoing review in addition to clear explanations, real examples, exercises that relate to everyday life and innovative online support. Written by an award-wining author recognized for his reader-friendly approach, this edition provides a brief review of core algebra topics and coverage of analytic geometry in three dimensions in addition to an introduction to concepts covered in calculus. "How Do You See It?" exercises let you practice applying concepts, while new Summarize features and Checkpoint questions reinforce your understanding of skills you need to better prepare for tests. In addition, "Review & Refresh" exercises and Skills Review videos help you strengthen previously learned math skills. You can even access no-cost homework support on the websites CalcChat.com, CalcView.com and LarsonPrecalculus.com and refine your abilities with WebAssign activities and practice.
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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. The Complex Plane. Trigonometric Form of a Complex Number. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. 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. Summary and Study Strategies. Review Exercises. Chapter Test. Cumulative Test for Chapters. Proofs in Mathematics. P.S. Problem Solving.
13. CONCEPTS IN STATISTICS.
Representing Data. Analyzing Data. Modeling Data. Summary and Study Strategies. 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.
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Ron Larson
Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also written numerous acclaimed textbooks, including the best-selling Calculus Series published by Cengage. He is the recipient of the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS, the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS and the 2017 William Holmes McGuffey Longevity Award for CALCULUS. He also received 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.
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NEW "REVIEW & REFRESH" EXERCISES offer cumulative review practice, drawn from current or prerequisite courses. An important part of the exercise set for each section, these specially designed exercises provide general skill review that prepares students to succeed both in the next section and throughout the text.
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NEW SKILLS REFRESHER VIDEOS provide timely support by re-visiting previously learned skills that students need in order to better understand upcoming concepts, examples or definitions.
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NEW "EXPLORING THE CONCEPTS" SECTIONS, VOCABULARY AND CONCEPT CHECKS build student confidence and help students at all levels develop a solid conceptual understanding. Concept Checks also ensure students have the foundational knowledge needed for future learning.
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REVISED SUMMARY AND STUDY STRATEGIES for each chapter highlight clear explanations and provide reader-friendly examples of key objectives. These learning features also walk students through the essential study skills to help them succeed in your course.
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UPDATED WEBASSIGN ONLINE RESOURCES provide you with the customizable tools at your fingertips to build students’ confidence and elevate their performance in your course and beyond. WebAssign offers built-in flexibility and control for you, the instructor, with high quality, affordable content and meaningful practice opportunities for your students.
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TEXT-SPECIFIC TUTORIAL VIDEOS are easily accessible for your students at Larson’s CalcView.com. These tutorials, created to work seamlessly for this 5th Edition of PRECALCULUS WITH LIMITS, provide additional instruction with stepped-out solutions for selected exercises.
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HELPFUL ONLINE LEARNING SUPPORT at Larson’s CalcChat.com provides your students with effective, no-cost online tutoring as well as solutions to all odd-numbered problems.
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"HOW DO YOU SEE IT?" EXERCISES in every section present real-life problems that students solve by visual inspection, using the concepts from the lesson.
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SIDE-BY-SIDE EXAMPLES visually demonstrate to students that problems can be solved in more than one way. Students also see how different methods--algebraic, graphical and numerical--yield the same result. This unique, side-by-side format also addresses the needs of your students' many different learning styles.
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ALGEBRA OF CALCULUS EXAMPLES AND EXERCISES throughout the text emphasize the various algebraic techniques that are used in calculus.
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THIS "WITH LIMITS" VERSION of Larson's award-winning PRECALCULUS text provides additional review and introductions students need to bridge specific gaps in readiness. This edition offers a brief ongoing review of core algebraic topics and covers analytic geometry in three dimensions while also introducing key concepts covered in calculus.
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