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Preliminaries I S PrecaLcu[us Review 2 2 Precalcutus Review I 11 The Cartesian Coordinate System 23 S Straight Lines 31 Chapter 1 Summary of Principal Formulas and Terms 46 Chapter 1 Concept Review Questions 46 Chapter Revew Exercises 47 Chapter 1 Before Moving On 48 Functions, Limits, and the Derivative 49 S Functions and Their Graphs 50 Using Technology: Graphing a Function 64 2 The Algebra of Functions 68 Functions and Mathematical Models 76 Using Technology: Finding the Points of Intersection of Two Graphs and Modeling 93 Limits 97 Using Technology: Finding the Limit of a Function 116 5 One-Sided Limits and Continuity 119 Using Technology: Finding the Points of Discontinuity of a Function 132 Derivative 135 Using Technology: Graphing a Function and Its Tangent Line 152 Chapter 2 Summary of Principal Formulas and Terms 155 Chapter 2 Concept Review Questions 155 SChapter 2 Rev ew Exercises 156 Chapter 2 Before Moving On 158 Basic Rules of Differentiation 160 Using Technology: Finding the Rate of Change of a Function 171 Sections marked with an asterisk are not prerequisites for later material . . .. . II I II I II I II I I I I I I I I I I I 1 1 KIM'I:i 3.2 The Product and Quotient Rules 174 Using Technology: The Product and Quotient Rules 183 3.3 The Chain Rule 185 Using Technology: Finding the Derivative of a Composite Function 196 3.4 Marginal Functions in Economics 197 3.5 Higher-Order Derivatives 212 PORTFOLIO: Steve Regenstreif 213 Using Technology: Finding the Second Derivative of a Function at a Given Point 219 *3.6 Implicit Differentiation and Related Rates 221 3.7 Differentials 232 Using Technology: Finding the Differential of a Function 240 Chapter 3 Summary of Principal Formulas and Terms 242 Chapter 3 Concept Review Questions 243 Chapter 3 Review Exercises 243 Chapter 3 Before Moving On 245 Applications of the Derivative 247 4.1 Applications of the First Derivative 248 Using Technology: Using the First Derivative to Analyze a Function 264 4.2 Applications of the Second Derivative 267 Using Technology: Finding the Inflection Points of a Function 283 4.3 Curve Sketching 285 Using Technology: Analyzing the Properties of a Function 298 4.4 Optimization I 300 Using Technology: Finding the Absolute Extrema of a Function 313 4.5 Optimization II 315 Chapter 4 Summary of Principal Terms 327 Chapter 4 Concept Review Questions 327 Chapter 4 Review Exercises 328 Chapter 4 Before Moving On 330 Exiponentia and Loga thmic Functions 331 5.1 Exponential Functions 332 Using Technology 338 5.2 Logarithmic Functions 339 5.3 Compound Interest 347 5.4 Differentiation of Exponential Functions 360 PORTFOLIO: Robert Derbenti 361 Using Technology 370 5.5 Differentiation of Logarithmic Functions 371 "*5.6 Exponential Functions as Mathematical Models 379 Using Technology: Analyzing Mathematical Models 389 Chapter 5 Summary of Principal Formulas and Terms 392 Chapter 5 Concept Review Questions 392 Chapter 5 Review Exercises 393 Chapter 5 Before Moving On 394 Integration 395 6.1 Antiderivatives and the Rules of Integration 396 6.2 Integration by Substitution 410 6.3 Area and the Definite Integral 420 6.4 The Fundamental Theorem of Calculus 429 Using Technology: Evaluating Definite Integrals 440 6.5 Evaluating Definite Integrals 441 Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions 450 6.6 Area between Two Curves 452 Using Technology: Finding the Area between Two Curves 463 "*6.7 Applications of the Definite Integral to Business and Economics 464 Using Technology: Business and Economic Applications 476 Chapter 6 Sunnmay of Principal Formulas and Terms 478 Chapter 6 Concept Review Questions 479 Chapter 6 Review Ecvxercises 479 Chapter 6 Before Moving On 482 Additional Topics in Integration 483 7.1 Integration by Parts 484 *7.2 Integration Using Tables of integrals 491 "*7.3 Numerical Integration 498 7.4 Improper Integrals 513 *7.5 Applications of Calculus to Probability 522 PORTFOLIO: Gary Li 530 Chapter 7 Summinay of Pi ucipal Formulas and lTerms 533 Chapter 7 Concept Review Questions 534 Chlapter 7 Review xercises 534 Chapter 7 BefobL Mlo ing, On 536 Calculus of Several Variables 537 8,1 Functions of Several Variables 538 8.2 Partial Derivatives 547 Using Jcchnolog,,: Fiindg Partial Derivatives at a Given Point 560 8.3 Maxima and Minima of Functions of Several Variables 561 PORTFOLIO: Kirk Hoiberg 564 8.4 The Method of Least Squares 572 Using Technology: Finding an Equation of a Least-Squares Line 581 8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers 583 8.6 Double Integrals 594 Chapter 8 Summary of Principal Formulas and Terms 608 Chapter 8 Concept Review Questions 608 Chapter 8 Review Everciser 609 Chapter 8 Before Moving On 610 Inverse Functions 611 Chapter Review Tests 619 Answers to Odd-Numbered Exercises 627 Answers to Chapter Review Tests 669 Index 671

Library of Congress subject headings for this publication: Calculus Textbooks, Social sciences Mathematics Textbooks