Larson Calculus: Early Transcendental Functions, 7th Edition

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


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


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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