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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
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