Chapter 1: Limits and Their Properties
1.1: A Preview of Calculus 42
1.2: Finding Limits Graphically and Numerically 48
1.3: Evaluating Limits Analytically 59
1.4: Continuity and One-Sided Limits 70
1.5: Infinite Limits 83
1: Review Exercises 91
1: Problem Solving
Chapter 2: Differentiation
2.1: The Derivative and the Tangent Line Problem 96
2.2: Basic Differentiation Rules and Rates of Change 106
2.3: Product and Quotient Rules and Higher-Order Derivatives 118
2.4: The Chain Rule 129
2.5: Implicit Differentiation 140
2.6: Related Rates 148
2: Review Exercises 157
2: Problem Solving
Chapter 3: Applications of Differentiation
3.1: Extrema on an Interval 162
3.2: Rolle's Theorem and the Mean Value Theorem 170
3.3: Increasing and Decreasing Functions and the First Derivative Test 177
3.4: Concavity and the Second Derivative Test 187
3.5: Limits at Infinity 195
3.6: A Summary of Curve Sketching 206
3.7: Optimization Problems 215
3.8: Newton's Method 225
3.9: Differentials 231
3: Review Exercises 238
3: Problem Solving
Chapter 4: Integration
4.1: Antiderivatives and Indefinite Integration 244
4.2: Area 254
4.3: Riemann Sums and Definite Integrals 266
4.4: The Fundamental Theorem of Calculus 277
4.5: Integration by Substitution 292
4.6: Numerical Integration 305
4: Review Exercises 312
4: Problem Solving
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
5.1: The Natural Logarithmic Function: Differentiation 318
5.2: The Natural Logarithmic Function: Integration 328
5.3: Inverse Functions 337
5.4: Exponential Functions: Differentiation and Integration 346
5.5: Bases Other than e and Applications 356
5.6: Inverse Trigonometric Functions: Differentiation 366
5.7: Inverse Trigonometric Functions: Integration 375
5.8: Hyperbolic Functions 383
5: Review Exercises 393
5: Problem Solving
Chapter 6: Differential Equations
6.1: Slope Fields and Euler's Method 398
6.2: Differential Equations: Growth and Decay 407
6.3: Separation of Variables and the Logistic Equation 415
6.4: First-Order Linear Differential Equations 424
6: Review Exercises 431
6: Problem Solving
Chapter 7: Applications of Integration
7.1: Area of a Region Between Two Curves 436
7.2: Volume: The Disk Method 446
7.3: Volume: The Shell Method 457
7.4: Arc Length and Surfaces of Revolution 466
7.5: Work 477
7.6: Moments, Centers of Mass, and Centroids 486
7.7: Fluid Pressure and Fluid Force 497
7: Review Exercises 503
7: Problem Solving
Chapter 8: Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1: Basic Integration Rules 508
8.2: Integration by Parts 515
8.3: Trigonometric Integrals 524
8.4: Trigonometric Substitution 533
8.5: Partial Fractions 542
8.6: Integration by Tables and Other Integration Techniques 561
8.7: Indeterminate Forms and L'Hopital's Rule 557
8.8: Improper Integrals 568
8: Review Exercises 579
8: Problem Solving
Chapter 9: Infinite Series
9.1: Sequences 584
9.2: Series and Convergence 595
9.3: The Integral Test and p-Series 605
9.4: Comparisons of Series 612
9.5: Alternating Series 619
9.6: The Ratio and Root Tests 627
9.7: Taylor Polynomials and Approximations 636
9.8: Power Series 647
9.9: Representation of Functions by Power Series 657
9.10: Taylor and Maclaurin Series 664
9: Review Exercises 676
9: Problem Solving
Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.1: Conics and Calculus 682
10.2: Plane Curves and Parametric Equations 696
10.3: Parametric Equations and Calculus 706
10.4: Polar Coordinates and Polar Graphs 715
10.5: Area and Arc Length in Polar Coordinates 725
10.6: Polar Equations of Conics and Kepler's Laws 734
10: Review Exercises 742
10: Problem Solving
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