# Larson Calculus: Early Transcendental Functions, 7th ... Larson Calculus: Early Transcendental ...

ISBN: 9781337552516 / 1337552518

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## Table of Contents

### Chapter 1

Preparation For Calculus

 1.1 Graphs and Models Exercises p.8 1.2 Linear Models and Rates of Change Exercises p.16 1.3 Functions and Their Graphs Exercises p.27 1.4 Review of Trigonometric Functions Exercises p.38 1.5 Inverse Functions Exercises p.48 1.6 Exponential and Logarithmic Functions Exercises p.57 Review Exercises p.60 Problem Solving p.63

### Chapter 2

Limits And Their Properties

 2.1 A Preview of Calculus Exercises p.71 2.2 Finding Limits Graphically and Numerically Exercises p.79 2.3 Evaluating Limits Analytically Exercises p.91 2.4 Continuity and One-Sided Limits Exercises p.103 2.5 Infinite Limits Exercises p.112 Review Exercises p.115 Problem Solving p.117

### Chapter 3

Differentiation

 3.1 The Derivative and the Tangent Line Problem Exercises p.127 3.2 Basic Differentiation Rules and Rates of Change Exercises p.139 3.3 Product and Quotient Rules and Higher-Order Derivatives Exercises p.150 3.4 The Chain Rule Exercises p.164 3.5 Implicit Differentiation Exercises p.175 3.6 Derivatives of Inverse Functions Exercises p.182 3.7 Related Rates Exercises p.190 3.8 Newton’s Method Exercises p.198 Review Exercises p.200 Problem Solving p.203

### Chapter 4

Applications Of Differentiation

 4.1 Extrema on an Interval Exercises p.211 4.2 Rolle’s Theorem and the Mean Value Theorem Exercises p.218 4.3 Increasing and Decreasing Functions and the First Derivative Test Exercises p.227 4.4 Concavity and the Second Derivative Test Exercises p.236 4.5 Limits at Infinity Exercises p.246 4.6 A Summary of Curve Sketching Exercises p.256 4.7 Optimization Problems Exercises p.266 4.8 Differentials Exercises p.276 Review Exercises p.278 Problem Solving p.281

### Chapter 5

Integration

 5.1 Antiderivatives and Indefinite Integration Exercises p.291 5.2 Area Exercises p.303 5.3 Riemann Sums and Definite Integrals Exercises p.313 5.4 The Fundamental Theorem of Calculus Exercises p.328 5.5 Integration by Substitution Exercises p.341 5.6 Indeterminate Forms and L’Hôpital’s Rule Exercises p.352 5.7 The Natural Logarithmic Function: Integration Exercises p.362 5.8 Inverse Trigonometric Functions: Integration Exercises p.370 5.9 Hyperbolic Functions Exercises p.380 Review Exercises p.383 Problem Solving p.385

### Chapter 6

Differential Equations

 6.1 Slope Fields and Euler’s Method Exercises p.393 6.2 Growth and Decay Exercises p.402 6.3 Separation of Variables Exercises p.413 6.4 The Logistic Equation Exercises p.422 6.5 First-Order Linear Differential Equations Exercises p.428 6.6 Predator-Prey Differential Equations Exercises p.436 Review Exercises p.438 Problem Solving p.441

### Chapter 7

Applications Of Integration

 7.1 Area of a Region Between Two Curves Exercises p.450 7.2 Volume: The Disk Method Exercises p.461 7.3 Volume: The Shell Method Exercises p.470 7.4 Arc Length and Surfaces of Revolution Exercises p.481 7.5 Work Exercises p.491 7.6 Moments, Centers of Mass, and Centroids Exercises p.502 7.7 Fluid Pressure and Fluid Force Exercises p.509 Review Exercises p.511 Problem Solving p.513

### Chapter 8

Integration Techniques And Improper Integrals

 8.1 Basic Integration Rules Exercises p.520 8.2 Integration by Parts Exercises p.529 8.3 Trigonometric Integrals Exercises p.538 8.4 Trigonometric Substitution Exercises p.547 8.5 Partial Fractions Exercises p.557 8.6 Numerical Integration Exercises p.564 8.7 Integration by Tables and Other Integration Techniques Exercises p.570 8.8 Improper Integrals Exercises p.579 Review Exercises p.583 Problem Solving p.585

### Chapter 9

Infinite Series

 9.1 Sequences Exercises p.596 9.2 Series and Convergence Exercises p.605 9.3 The Integral Test and p-Series Exercises p.613 9.4 Comparisons of Series Exercises p.620 9.5 Alternating Series Exercises p.629 9.6 The Ratio and Root Tests Exercises p.637 9.7 Taylor Polynomials and Approximations Exercises p.648 9.8 Power Series Exercises p.658 9.9 Representation of Functions by Power Series Exercises p.666 9.10 Taylor and Maclaurin Series Exercises p.677 Review Exercises p.680 Problem Solving p.683

### Chapter 10

Conics, Parametric Equations, And Polar Coordinates

 10.1 Conics and Calculus Exercises p.696 10.2 Plane Curves and Parametric equations Exercises p.707 10.3 Parametric Equations and Calculus Exercises p.715 10.4 Polar Coordinates and Polar Graphs Exercises p.726 10.5 Area and Arc Length in Polar Coordinates Exercises p.735 10.6 Polar Equations of Conics and Kepler’s Laws Exercises p.743 Review Exercises p.746 Problem Solving p.749

### Chapter 11

Vectors And The Geometry Of Space

 11.1 Vectors in the Plane Exercises p.759 11.2 Space Coordinates and Vectors in Space Exercises p.767 11.3 The Dot Product of Two Vectors Exercises p.777 11.4 The Cross Product of Two Vectors in Space Exercises p.785 11.5 Lines and Planes in Space Exercises p.794 11.6 Surfaces in Space Exercises p.806 11.7 Cylindrical and Spherical Coordinates Exercises p.813 Review Exercises p.815 Problem Solving p.817

### Chapter 12

Vector-Valued Functions

 12.1 Vector-Valued Functions Exercises p.825 12.2 Differentiation and Integration of Vector-Valued Functions Exercises p.834 12.3 Velocity and Acceleration Exercises p.842 12.4 Tangent Vectors and Normal Vectors Exercises p.852 12.5 Arc Length and Curvature Exercises p.864 Review Exercises p.867 Problem Solving p.869

### Chapter 13

Functions Of Several Variables

 13.1 Introduction to Functions of Several Variables Exercises p.880 13.2 Limits and Continuity Exercises p.891 13.3 Partial Derivatives Exercises p.900 13.4 Differentials Exercises p.909 13.5 Chain Rules for Functions of Several Variables Exercises p.917 13.6 Directional Derivatives and Gradients Exercises p.928 13.7 Tangent Planes and Normal Lines Exercises p.937 13.8 Extrema of Functions of Two Variables Exercises p.946 13.9 Applications of Extrema Exercises p.953 13.10 Lagrange Multipliers Exercises p.962 Review Exercises p.964 Problem Solving p.967

### Chapter 14

Multiple Integration

 14.1 Iterated Integrals and Area in the Plane Exercises p.976 14.2 Double Integrals and Volume Exercises p.987 14.3 Change of Variables: Polar Coordinates Exercises p.995 14.4 Center of Mass and Moments of Inertia Exercises p.1004 14.5 Surface Area Exercises p.1011 14.6 Triple Integrals and Applications Exercises p.1021 14.7 Triple Integrals in Other Coordinates Exercises p.1029 14.8 Change of Variables: Jacobians Exercises p.1036 Review Exercises p.1038 Problem Solving p.1041

### Chapter 15

Vector Analysis

 15.1 Vector Fields Exercises p.1053 15.2 Line Integrals Exercises p.1065 15.3 Conservative Vector Fields and Independence of Path Exercises p.1076 15.4 Green’s Theorem Exercises p.1085 15.5 Parametric Surfaces Exercises p.1095 15.6 Surface Integrals Exercises p.1108 15.7 Divergence Theorem Exercises p.1116 15.8 Stokes’s Theorem Exercises p.1123 Review Exercises p.1124 Problem Solving p.1127

### Chapter Appendix C

Precalculus Review

 C.1 Real Numbers and the Real Number Line Exercises p.A14 C.2 The Cartesian Pllane Exercises p.A21
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