PRECALCULUS WITH LIMITS provides a brief algebra review of core topics and an introduction to concepts covered in calculus. The Fourth Edition incorporates real-world applications, ongoing review, and innovative technology. How Do You See It? exercises let you practice applying the concepts, and Summarize and Checkpoint questions reinforce understanding of the skill sets to help you prepare for tests.
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. The Complex Plane. 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.
13. CONCEPTS IN STATISTICS.
Representing Data. Analyzing Data. Modeling Data. 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.
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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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Stepped-out solution videos with instruction are available at CalcView.com for selected exercises throughout the text. The selected textbook exercises will have a QR code next to the exercise number for easy access via a smart phone.
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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.
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ENHANCED WEBASSIGN: PRECALCULUS WITH LIMITS, Fourth Edition, is fully supported by Enhanced WebAssign (EWA), the powerful online homework and course management system that engages students in learning the math. EWA includes new end-of-chapter exercises, animated simulations, and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.
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The Student Companion Website features chapter projects, data tables, assessments, study tools, video solutions, and more to support students outside the text.
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Up-to-the-minute homework support through CalcChat.com, an independent website, provides students with free, up-to-the-minute homework support, including solutions to all odd-numbered problems in the text.
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Algebra Helps features direct students to sections of the textbook where they can review algebra skills needed to master the current topic.
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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.
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Algebra of Calculus examples and exercises throughout the text emphasize various algebraic techniques used in calculus.
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Original Checkpoint Problems encourage immediate practice and check students' understanding of the concepts in the paired example.
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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 in the lesson.
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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--algebraic, graphical, and numerical--yield the same result. The side-by-side format also addresses many different learning styles.
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Larson's PRECALCULUS WITH LIMITS is ideal for a two-term course.
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