Calculus 9th Edition Dale Varberg, Edwin Purcell, & Steve Rigdon

Jul 18, 2026

Uploaded by Aurora

This document is the 9th edition of the textbook "Calculus" by Dale Varberg, Edwin Purcell, and Steve Rigdon. The book provides a comprehensive treatment of calculus concepts, theories, and applications. It is designed to guide students through the fundamental principles of differential and integral calculus, including topics such as limits, derivatives, and their applications in analyzing functions and solving optimization problems. The text also delves into sequences and series, multivariable calculus, and differential equations, offering a rigorous yet accessible approach to the subject matter. The edition likely incorporates updated pedagogical features, examples, and exercises to enhance student learning and comprehension. The visual elements, such as the provided images, suggest the book might feature geometric illustrations or theoretical diagrams to aid in understanding complex mathematical concepts. This textbook serves as a foundational resource for students pursuing higher education in mathematics, science, engineering, and related fields, equipping them with the analytical tools necessary for advanced study and problem-solving.

LanguageEnglish

CategoryExam

FormatPDF

Pages797

Reading Time33 h 28 min

AccessFree to download

MVIEIMTKCalculus Varberg Purcell Rigdon Contents Preface ix Preliminaries 1 0.1 Real Numbers,Estimation,and Logic 1 0.2 Inequalities and Absolute Values 8 0.3 The Rectangular Coordinate System 16 0.4 Graphs of Equations 24 0.5 Functions and Their Graphs 29 0.6 Operations on Functions 35 0.7 Trigonometric Functions 41 0.8 Chapter Review 51Review and Preview Problems 54 Limits 55 1.1 Introduction to Limits 55 1.2 Rigorous Study of Limits 61 1.3 Limit Theorems 68 1.4 Limits Involving Trigonometric Functions 73 1.5 Limits at Infinity;Infinite Limits 77 1.6 Continuity of Functions 82 1.7 Chapter Review 90Review and Preview Problems 92 2 The Derivative 93 2.1 Two Problems with One Theme 93 2.2 The Derivative 100 2.3 Rules for Finding Derivatives 107 2.4 Derivatives of Trigonometric Functions 114 2.5 The Chain Rule 118 2.6 Higher-Order Derivatives 125 2.7 Implicit Differentiation 130 2.8 Related Rates 135 2.9 Differentials and Approximations 142 2.10 Chapter Review 147 Review and Preview Problems 150 Applications of the Derivative 151 3.1 Maxima and Minima 151 3.2 Monotonicity and Concavity 155 3.3 Local Extrema and Extrema on Open Intervals 162 3.4 Practical Problems 167 3.5 Graphing Functions Using Calculus 178 3.6 The Mean Value Theorem for Derivatives 185 3.7 Solving Equations Numerically 190 3.8 Antiderivatives 197 3.9 Introduction to Differential Equations 203 3.10 Chapter Review 209Review and Preview Problems 214 4 The Definite Integral 215 4.1 Introduction to Area 215 4.2 The Definite Integral 224 4.3 The First Fundamental Theorem of Calculus 232 4.4 The Second Fundamental Theorem of Calculus and the Methodof Substitution 243 4.5 The Mean Value Theorem for Integrals and theUse of Symmetry 253 4.6 Numerical Integration 260 4.7 Chapter Review 270 Review and Preview Problems 274 二Applications of the Integral 275 5.1 The Area of a Plane Region 275 5.2 Volumes of Solids:Slabs,Disks,Washers 281 5.3 Volumes of Solids of Revolution:Shells 288 5.4 Length of a Plane Curve 294 5.5 Work and Fluid Force 301 5.6 Moments and Center of Mass 308 5.7 Probability and Random Variables 316 5.8 Chapter Review 322 Review and Preview Problems 324 Transcendental Functions 325 6.1 The Natural Logarithm Function 325 6.2 Inverse Functions and Their Derivatives 331 6.3 The Natural Exponential Function 337 6.4 General Exponential and Logarithmic Functions 342 6.5 Exponential Growth and Decay 347 6.6 First-Order Linear Differential Equations 355 6.7 Approximations for Differential Equations 359 6.8 The Inverse Trigonometric Functions and Their Derivatives 365 6.9 The Hyperbolic Functions and Their Inverses 374 6.10 Chapter Review 380Review and Preview Problems 382 7Techniques of Integration 383 7.1 Basic Integration Rules 383 7.2 Integration by Parts 387 7.3 Some Trigonometric Integrals 393 7.4 Rationalizing Substit

FAQs

What is the primary subject of this document?

This document is the 9th edition of the textbook "Calculus" by Dale Varberg, Edwin Purcell, and Steve Rigdon.

What key areas of calculus does the textbook cover?

The textbook covers fundamental principles of differential and integral calculus, including limits, derivatives, sequences, series, multivariable calculus, and differential equations.

What is the intended audience for this textbook?

This textbook is designed for students pursuing higher education in mathematics, science, engineering, and related fields.

Jul 18, 2026

Uploaded by Aurora