# Calculus: Early Transcendentals, 8th Edition Calculus: Early Transcendentals, 8th Edition 8th Edition | ISBN: 9781305482463 / 1305482468

10,216

expert-verified solutions in this book  8th Edition | ISBN: 9781305482463 / 1305482468

10,216

expert-verified solutions in this book

### Chapter 1

Functions And Models

 1.1 Four Ways to Represent a Function Exercises p.19 1.2 Mathematical Models: A Catalog of Essential Functions Exercises p.33 1.3 New Functions from Old Functions Exercises p.42 1.4 Exponential Functions Exercises p.53 1.5 Inverse Functions and Logarithms Exercises p.66 Review: Concept Check p.68 Review: True-False Quiz p.69 Review: Exercises p.69 Problems Plus p.76

### Chapter 2

Limits And Derivatives

 2.1 The Tangent and Velocity Problems Exercises p.82 2.2 The Limit of a Function Exercises p.92 2.3 Calculating Limits Using the Limit Laws Exercises p.102 2.4 The Precise Definition of a Limit Exercises p.113 2.5 Continuity Exercises p.124 2.6 Limits at Infinity; Horizontal Asymptotes Exercises p.137 2.7 Derivatives and Rates of Change Exercises p.148 2.8 The Derivative as a Function Exercises p.160 Review: Concept Check p.165 Review: True-False Quiz p.166 Review: Exercises p.166 Problems Plus p.169

### Chapter 3

Differentiation Rules

 3.1 Derivatives of Polynomials and Exponential Functions Exercises p.180 3.2 The Product and Quotient Rules Exercises p.188 3.3 Derivatives of Trigonometric Functions Exercises p.196 3.4 The Chain Rule Exercises p.204 3.5 Implicit Differentiation Exercises p.215 3.6 Derivatives of Logarithmic Functions Exercises p.223 3.7 Rates of Change in the Natural and Social Sciences Exercises p.233 3.8 Exponential Growth and Decay Exercises p.242 3.9 Related Rates Exercises p.249 3.10 Linear Approximations and Differentials Exercises p.256 3.11 Hyperbolic Functions Exercises p.264 Review: Concept Check p.266 Review: True-False Quiz p.266 Review: Concept Check p.267 Problems Plus p.271

### Chapter 4

Applications Of Differentiation

 4.1 Maximum and Minimum Values Exercises p.283 4.2 The Mean Value Theorem Exercises p.291 4.3 How Derivatives Affect the Shape of a Graph Exercises p.300 4.4 Indeterminate Forms and l'Hospital's Rule Exercises p.311 4.5 Summary of Curve Sketching Exercises p.321 4.6 Graphing with Calculus and Calculators Exercises p.329 4.7 Optimization Problems Exercises p.336 4.8 Newton's Method Exercises p.348 4.9 Antiderivatives Exercises p.355 Review: Concept Check p.358 Review: True-False Quiz p.358 Review: Exercises p.359 Problems Plus p.363

### Chapter 5

Integrals

 5.1 Areas and Distances Exercises p.375 5.2 The Definite Integral Exercises p.388 5.3 The Fundamental Theorem of Calculus Exercises p.399 5.4 Indefinite Integrals and the Net Change Theorem Exercises p.408 5.5 The Substitution Rule Exercises p.418 Review: Concept Check p.421 Review: True-False Quiz p.421 Review: Exercises p.422 Problems Plus p.425

### Chapter 6

Applications Of Integration

 6.1 Areas Between Curves Exercises p.434 6.2 Volumes Exercises p.446 6.3 Volumes by Cylindrical Shells Exercises p.453 6.4 Work Exercises p.458 6.5 Average Value of a Function Exercises p.463 Review: Concept Check p.466 Review: Exercises p.466 Problems Plus p.468

### Chapter 7

Techniques Of Integration

 7.1 Integration by Parts Exercises p.476 7.2 Trigonometric Integrals Exercises p.484 7.3 Trigonometric Substitution Exercises p.491 7.4 Integration of Rational Functions by Partial Fractions Exercises p.501 7.5 Strategy for Integration Exercises p.507 7.6 Integration Using Tables and Computer Algebra Systems Exercises p.512 7.7 Approximate Integration Exercises p.524 7.8 Improper Integrals Exercises p.534 Review: True-False Quiz p.537 Review: Concept Check p.537 Review: Exercises p.537 Problems Plus p.541

### Chapter 8

Further Applications Of Integration

 8.1 Arc Length Exercises p.548 8.2 Area of a Surface of Revolution Exercises p.555 8.3 Applications to Physics and Engineering Exercises p.565 8.4 Applications to Economics and Biology Exercises p.572 8.5 Probability Exercises p.579 Review: Concept Check p.581 Review: Exercises p.581 Problems Plus p.583

### Chapter 9

Differential Equations

 9.1 Modeling with Differential Equations Exercises p.590 9.2 Direction Fields and Euler's Method Exercises p.597 9.3 Separable Equations Exercises p.605 9.4 Models for Population Growth Exercises p.617 9.5 Linear Equations Exercises p.625 9.6 Predator-Prey Systems Exercises p.631 Review: Concept Check p.634 Review: True-False Quiz p.634 Review: Exercises p.634 Problems Plus p.637

### Chapter 10

Parametric Equations And Polar Coordinates

 10.1 Curves Defined by Parametric Equations Exercises p.645 10.2 Calculus with Parametric Curves Exercises p.655 10.3 Polar Coordinates Exercises p.666 10.4 Areas and Lengths in Polar Coordinates Exercises p.672 10.5 Conic Sections Exercises p.680 10.6 Conic Sections in Polar Coordinates Exercises p.688 Review: True-False Quiz p.689 Review: Concept Check p.689 Review: Exercises p.690 Problems Plus p.692

### Chapter 11

Infinite Sequences And Series

 11.1 Sequences Exercises p.704 11.2 Series Exercises p.715 11.3 The Integral Test and Estimates of Sums Exercises p.725 11.4 The Comparison Tests Exercises p.731 11.5 Alternating Series Exercises p.736 11.6 Absolute Convergence and the Ratio and Root Tests Exercises p.742 11.7 Strategy for Testing Series Exercises p.746 11.8 Power Series Exercises p.751 11.9 Representations of Functions as Power Series Exercises p.757 11.10 Taylor and Maclaurin Series Exercises p.771 11.11 Applications of Taylor Polynomials Exercises p.780 Review: Concept Check p.784 Review: True-False Quiz p.784 Review: Exercises p.785 Problems Plus p.787

### Chapter 12

Vectors And The Geometry Of Space

 12.1 Three-Dimensional Coordinate Systems Exercises p.796 12.2 Vectors Exercises p.805 12.3 The Dot Product Exercises p.812 12.4 The Cross Product Exercises p.821 12.5 Equations of Lines and Planes Exercises p.831 12.6 Cylinders and Quadric Surfaces Exercises p.839 Review: Concept Check p.841 Review: True-False Quiz p.842 Review: Exercises p.842 Problems Plus p.844

### Chapter 13

Vector Functions

 13.1 Vector Functions and Space Curves Exercises p.853 13.2 Derivatives and Integrals of Vector Functions Exercises p.860 13.3 Arc Length and Curvature Exercises p.868 13.4 Motion in Space: Velocity and Acceleration Exercises p.878 Review: True-False Quiz p.881 Review: Concept Check p.881 Review: Exercises p.882 Problems Plus p.884

### Chapter 14

Partial Derivatives

 14.1 Functions of Several Variables Exercises p.899 14.2 Limits and Continuity Exercises p.910 14.3 Partial Derivatives Exercises p.923 14.4 Tangent Planes and Linear Approximations Exercises p.934 14.5 The Chain Rule Exercises p.943 14.6 Directional Derivatives and the Gradient Vector Exercises p.956 14.7 Maximum and Minimum Values Exercises p.967 14.8 Lagrange Multipliers Exercises p.977 Review: Concept Check p.981 Review: True-False Quiz p.982 Review: Exercises p.982 Problems Plus p.985

### Chapter 15

Multiple Integrals

 15.1 Double Integrals over Rectangles Exercises p.999 15.2 Double Integrals over General Regions Exercises p.1008 15.3 Double Integrals in Polar Coordinates Exercises p.1014 15.4 Applications of Double Integrals Exercises p.1024 15.5 Surface Area Exercises p.1028 15.6 Triple Integrals Exercises p.1037 15.7 Triple Integrals in Cylindrical Coordinates Exercises p.1043 15.8 Triple Integrals in Spherical Coordinates Exercises p.1049 15.9 Change of Variables in Multiple Integrals Exercises p.1060 Review: Concept Check p.1061 Review: True-False Quiz p.1061 Review: Exercises p.1062

### Chapter 16

Vector Calculus

 Problems Plus p.1065 16.1 Vector Fields Exercises p.1073 16.2 Line Integrals Exercises p.1084 16.3 The Fundamental Theorem for Line Integrals Exercises p.1094 16.4 Green's Theorem Exercises p.1101 16.5 Curl and Divergence Exercises p.1109 16.6 Parametric Surfaces and Their Areas Exercises p.1120 16.7 Surface Integrals Exercises p.1132 16.8 Stoke's Theorem Exercises p.1139 16.9 The Divergence Theorem Exercise p.1145 Review: Concept Check p.1148 Review: True-False Quiz p.1148 Review: Exercises p.1149 Problems Plus p.1151

### Chapter 17

Second-Order Differential Equations

 17.1 Second-Order Linear Equations Exercises p.1160 17.2 Nonhomogeneous Linear Equations Exercises p.1167 17.3 Applications of Second-Order Differential Equations Exercises p.1175 17.4 Series Solutions Exercises p.1180 Review: True-False Quiz p.1181 Review: Concept Check p.1181 Review: Exercises p.1181
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