# Stewart Essential Calculus Early Transcendentals, 2nd Edition Stewart Essential Calculus Early Transcendentals, 2nd Edition

2nd Edition | ISBN: 9781133112280 / 1133112285

6,933

expert-verified solutions in this book

2nd Edition | ISBN: 9781133112280 / 1133112285

6,933

expert-verified solutions in this book

### Chapter 1

Functions And Limits

 1.1 Functions and Their Representations Exercises p.8 1.2 A Catalog of Essential Functions Exercises p.21 1.3 The Limit of a Function Exercises p.33 1.4 Calculating Limits Exercises p.43 1.5 Continuity Exercises p.54 1.6 Limits Involving Infinity Exercises p.67 Chapter 1 Review (Concept Check) p.70 Chapter 1 Review (True-False Quiz) p.70 Chapter 1 Review (Exercises) p.71

### Chapter 2

Derivatives

 2.1 Derivatives and Rates of Change Exercises p.80 2.2 The Derivative as a Function Exercises p.92 2.3 Basic Differentiation Formulas Exercises p.105 2.4 The Product and Quotient Rules Exercises p.112 2.5 The Chain Rule Exercises p.120 2.6 Implicit Differentiation Exercises p.127 2.7 Related Rates Exercises p.132 2.8 Linear Approximations and Differentials Exercises p.138 Chapter 2 Review (Concept Check) p.140 Chapter 2 Review (True-False Quiz) p.140 Chapter 2 Review (Exercises) p.141

### Chapter 3

Inverse Functions

 3.1 Exponential Functions Exercises p.150 3.2 Inverse Functions and Logarithms Exercises p.161 3.3 Derivatives of Logarithmic and Exponential Functions Exercises p.169 3.4 Exponential Growth and Decay Exercises p.177 3.5 Inverse Trigonometric Functions Exercises p.183 3.6 Hyperbolic Functions Exercises p.189 3.7 Indeterminate Forms and L'Hôpital's Rule Exercises p.197 Chapter 3 Review (Concept Check) p.199 Chapter 3 Review (True-False Quiz) p.199 Chapter 3 Review (Exercises) p.200

### Chapter 4

Applications Of Differentiation

 4.1 Maximum and Minimum Values Exercises p.208 4.2 The Mean Value Theorem Exercises p.215 4.3 Derivatives and the Shapes of Graphs Exercises p.222 4.4 Curve Sketching Exercises p.230 4.5 Optimization Problems Exercises p.238 4.6 Newton's Method Exercises p.245 4.7 Antiderivatives Exercises p.252 Chapter 4 Review (Concept Check) p.253 Chapter 4 Review (True-False Quiz) p.254 Chapter 4 Review (Exercises) p.254

### Chapter 5

Integrals

 5.1 Areas and Distances Exercises p.266 5.2 The Definite Integral Exercises p.279 5.3 Evaluating Definite Integrals Exercises p.289 5.4 The Fundamental Theorem of Calculus Exercises p.298 5.5 The Substitution Rule Exercises p.306 Chapter 5 Review (Concept Check) p.308 Chapter 5 Review (True-False Quiz) p.308 Chapter 5 Review (Exercises) p.309

### Chapter 6

Techniques Of Integration

 6.1 Integration by Parts Exercises p.316 6.2 Trigonometric Integrals and Substitutions Exercises p.326 6.3 Partial Fractions Exercises p.334 6.4 Integration with Tables and Computer Algebra Systems Exercises p.340 6.5 Approximate Integration Exercises p.350 6.6 Improper Integrals Exercises p.360 Chapter 6 Review (Concept Check) p.362 Chapter 6 Review (True-False Quiz) p.362 Chapter 6 Review (Exercises) p.363

### Chapter 7

Applications Of Integration

 7.1 Areas between Curves Exercises p.369 7.2 Volumes Exercises p.378 7.3 Volumes by Cylindrical Shells Exercises p.384 7.4 Arc Length Exercises p.391 7.5 Area of a Surface of Revolution Exercises p.397 7.6 Applications to Physics and Engineering Exercises p.408 7.7 Differential Equations Exercises p.418 Chapter 7 Review (Concept Check) p.421 Chapter 7 Review (Exercises) p.422

### Chapter 8

Series

 8.1 Sequences Exercises p.434 8.2 Series Exercises p.443 8.3 The Integral and Comparison Tests Exercises p.452 8.4 Other Convergence Tests Exercises p.463 8.5 Power Series Exercises p.468 8.6 Representing Functions as Power Series Exercises p.474 8.7 Taylor and Maclaurin Series Exercises p.487 8.8 Applications of Taylor Polynomials Exercises p.494 Chapter 8 Review (Concept Check) p.497 Chapter 8 Review (True-False Quiz) p.497 Chapter 8 Review (Exercises) p.498

### Chapter 9

Parametric Equations And Polar Coordinates

 9.1 Parametric Curves Exercises p.505 9.2 Calculus with Parametric Curves Exercises p.513 9.3 Polar Coordinates Exercises p.522 9.4 Areas and Lengths in Polar Coordinates Exercises p.528 9.5 Conic Sections in Polar Coordinates Exercises p.534 Chapter 9 Review (Concept Check) p.535 Chapter 9 Review (True-False Quiz) p.535 Chapter 9 Review (Exercises) p.535

### Chapter 10

Vectors And The Geometry Of Space

 10.1 Three-Dimensional Coordinate Systems Exercises p.541 10.2 Vectors Exercises p.549 10.3 The Dot Product Exercises p.556 10.4 The Cross Product Exercises p.564 10.5 Equations of Lines and Planes Exercises p.572 10.6 Cylinders and Quadric Surfaces Exercises p.579 10.7 Vector Functions and Space Curves Exercises p.589 10.8 Arc Length and Curvature Exercises p.598 10.9 Motion in Space: Velocity and Acceleration Exercises p.608 Chapter 10 Review (Concept Check) p.610 Chapter 10 Review (True-False Quiz) p.611 Chapter 10 Review (Exercises) p.612

### Chapter 11

Partial Derivatives

 11.1 Functions and Several Variables Exercises p.623 11.2 Limits and Continuity Exercises p.632 11.3 Partial Derivatives Exercises p.638 11.4 Tangent Places and Linear Approximations Exercises p.648 11.5 The Chain Rule Exercises p.656 11.6 Directional Derivatives and the Gradient Vector Exercises p.667 11.7 Maximum and Minimum Values Exercises p.675 11.8 Lagrange Multipliers Exercises p.683 Chapter 11 Review (Concept Check) p.685 Chapter 11 Review (True-False Quiz) p.685 Chapter 11 Review (Exercises) p.686

### Chapter 12

Multiple Integrals

 12.1 Double Integrals over Rectangles Exercises p.698 12.2 Double Integrals over General Regions Exercises p.707 12.3 Double Integrals in Polar Coordinates Exercises p.713 12.4 Applications of Double Integrals Exercises p.720 12.5 Triple Integrals Exercises p.728 12.6 Triple Integrals in Cylindrical Coordinates Exercises p.734 12.7 Triple Integrals in Spherical Coordinates Exercises p.740 12.8 Change of Variables in Multiple Integrals Exercises p.749 Chapter 12 Review (Concept Check) p.751 Chapter 12 Review (True-False Quiz) p.751 Chapter 12 Review (Exercises) p.752

### Chapter 13

Vector Calculus

 13.1 Vector Fields Exercises p.760 13.2 Line Integral Exercises p.770 13.3 The Fundamental Theorem for Line Integrals Exercises p.780 13.4 Green's Theorem Exercises p.787 13.5 Curl and Divergence Exercises p.795 13.6 Parametric Surfaces and Their Areas Exercises p.805 13.7 Surface Integrals Exercises p.816 13.8 Stoke's Theorem Exercises p.822 13.9 The Divergence Theorem Exercises p.829 Chapter 13 Review (Concept Check) p.830 Chapter 13 Review (True-False Quiz) p.831 Chapter 13 Review (Exercises) p.831