Calculus: A Complete Course, 7th Edition Calculus: A Complete Course, 7th Edition

Calculus: A Complete Course, 7th Edition

7th Edition | ISBN: 9780321549280 / 0321549287


expert-verified solutions in this book

Calculus: A Complete Course, 7th Edition
Buy on

7th Edition | ISBN: 9780321549280 / 0321549287


expert-verified solutions in this book

Buy on

Table of Contents

Chapter P


P-1 Real Numbers and the Real Line Exercises p.10
P-2 Cartesian Coordinates in the Plane Exercises p.16
P-3 Graphs of Quadratic Equations Exercises p.22
P-4 Functions and Their Graphs Exercises p.32
P-5 Combining Functions to Make Functions Exercises p.38
P-6 Polynomials and Rational Functions Exercises p.44
P-7 The Trigonometric Functions Exercises p.56

Chapter 1

Limits And Continuity

1-1 Examples of Velocity, Growth Rate, and Area Exercises p.62
1-2 Limits of Functions Exercises p.70
1-3 Limits at Infinity and Infinite Limits Exercises p.77
1-4 Continuity Exercises p.86
1-5 The Formal Definition of Limit Exercises p.91
Review Exercises p.92
Challenge Problems p.93

Chapter 2


2-1 Tangent Lines and Their Slopes Exercises p.99
2-2 The Derivative Exercises p.106
2-3 Differentiation Rules Exercises p.114
2-4 The Chain Rule Exercises p.119
2-5 Derivatives of Trigonometric Functions Exercises p.124
2-6 Higher-Order Derivatives Exercises p.129
2-7 Using Differentials and Derivatives Exercises p.134
2-8 The Mean-Value Theorem Exercises p.142
2-9 Implicit Differentiation Exercises p.147
2-10 Antiderivatives and Initial-Valued Problems Exercises p.153
2-11 Velocity and Acceleration Exercises p.159
Review Exercises p.160
Challenge Problems p.161

Chapter 3

Transcendental Functions

3-1 Inverse Functions Exercises p.169
3-2 Exponential and Logarithmic Functions Exercises p.173
3-3 The Natural Logarithm and Exponential Exercises p.181
3-4 Growth and Decay Exercises p.188
3-5 The Inverse Trigonometric Functions Exercises p.197
3-6 Hyperbolic Functions Exercises p.202
3-7 Second-Order Linear Des with Constant Coefficients Exercises p.209
Review Exercises p.210
Challenge Problems p.211

Chapter 4

More Applications Of Differentiation

4-1 Related Rates Exercises p.217
4-2 Finding Roots of Equations Exercises p.226
4-3 Indeterminate Forms Exercises p.232
4-4 Extreme Values Exercises p.238
4-5 Concavity and Inflections Exercises p.243
4-6 Sketching the Graphs of a Function Exercises p.251
4-7 Graphing with Computers Exercises p.257
4-8 Extreme-Value Problems Exercises p.263
4-9 Linear Approximations Exercises p.271
4-10 Taylor Polynomials Exercises p.279
4-11 Roundoff Error, Truncation Error, and Computers Exercises p.283
Review Exercises p.284
Challenge Problems p.285

Chapter 5


5-1 Sums and Sigma Notation Exercises p.292
5-2 Areas as Limits of Sums Exercises p.298
5-3 The Definite Integral Exercises p.304
5-4 Properties of the Definite Integral Exercises p.310
5-5 The Fundamental Theorem of Calculus Exercises p.315
5-6 The Method of Substitution Exercises p.323
5-7 Areas of Plane Regions Exercises p.327
Review Exercises p.328
Challenge Problems p.329

Chapter 6

Techniques Of Integration

6-1 Integration by Parts Exercises p.336
6-2 Integrals of Rational Functions Exercises p.345
6-3 Inverse Substitutions Exercises p.352
6-4 Other Methods for Evaluating Integrals Exercises p.358
6-5 Improper Integrals Exercises p.366
6-6 The Trapezoid and Midpoint Rules Exercises p.374
6-7 Simson's Rule Exercises p.379
6-8 Other Aspects of Approximate Integration Exercises p.385
Review Exercises p.387
Other Review Problems p.388
Challenge Problems p.388

Chapter 7

Applications Of Integration

7-1 Volumes by Slicing-Solids of Revolution Exercises p.398
7-2 More Volumes by Slicing Exercises p.402
7-3 Arc Length and Surface Exercises p.409
7-4 Mass, Moments, and Centre of Mass Exercises p.416
7-5 Centroids Exercises p.421
7-6 Other Physical Applications Exercises p.428
7-7 Applications in Business, Finance, and Ecology Exercises p.432
7-8 Probability Exercises p.444
7-9 First-order Differential Equations Exercises p.452
Review Exercises p.453
Challenge Problems p.454

Chapter 8

Conics, Parametric Curves, And Polar Curves

8-1 Conics Exercises p.467
8-2 Parametric Curves Exercises p.473
8-3 Smooth Parametric Curves and their Slopes Exercises p.478
8-4 Arc lengths and Areas for Parametric Curves Exercises p.482
8-5 Polar Coordinates and Polar Curves Exercises p.488
8-6 Slopes, Areas, and Arc Lengths for Polar Curves Exercises p.492
Review Exercises p.493
Challenge Problems p.493

Chapter 9

Sequences, Series, And Power Series

9-1 Sequences and Convergence Exercises p.502
9-2 Infinite Series Exercises p.509
9-2 Convergence Tests for Positive Series Exercises p.519
9-4 Absolute and Conditional Convergence Exercises p.525
9-5 Power Series Exercises p.536
9-6 Taylor and Maclaurin Series Exercises p.545
9-7 Applications of Taylor and Maclaurin Series Exercises p.549
9-8 The Binomial Theorem and Binomial Series Exercises p.552
9-9 Fourier Series Exercises p.558
Review Exercises p.559
Challenge Problems p.560

Chapter 10

Vectors And Coordinate Geometry In 3-Space

10-1 Analytic Geometry in Three Dimensions Exercises p.567
10-2 Vectors Exercises p.576
10-3 The Cross Product in 3-Space Exercises p.584
10-4 Planes and Lines Exercises p.592
10-5 Quadric Surfaces Exercises p.596
10-6 Cylindrical and Spherical Coordinates Exercises p.600
10-7 A Little Linear Algebra Exercises p.609
10-8 Using Maple for Vector and Matrix Calculations Exercises p.618
Review Exercises p.619
Challenge Problems p.619

Chapter 11

Vector Functions And Curves

11-1 Vector Functions of One Variable Exercises p.627
11-2 Some Applications of Vector Differentiation Exercises p.634
11-3 Curves and Parametrizations Exercises p.641
11-4 Curvature, Torsion, and the Frenet Frame Exercises p.649
11-5 Curvature and Torsion for General Parametrizations Exercises p.655
11-6 Kepler's Laws of Planetary Motion Exercises p.664
Review Exercises p.666
Challenge Problems p.667

Chapter 12

Partial Differentiation

12-1 Functions of Several Variables Exercises p.675
12-2 Limits and Continuity Exercises p.680
12-3 Partial Derivatives Exercises p.687
12-4 Higher-Order Derivatives Exercises p.692
12-5 The Chain Rule Exercises p.702
12-6 Linear Approximations, Differentiability, and Differentials Exercises p.712
12-7 Gradients and Directional Derivatives Exercises p.723
12-8 Implicit Functions Exercises p.734
12-9 Taylor Series and Approximations Exercises p.740
Review Exercises p.740
Challenge Problems p.741

Chapter 13

Applications Of Partial Derivatives

13-1 Extreme Values Exercises p.750
13-2 Extreme Values of Functions Defined on Restricted Domains Exercises p.756
13-3 Lagrange Multipliers Exercises p.764
13-4 The Method of Least Squares Exercises p.770
13-5 Parametric Problems Exercises p.779
13-6 Newton's Method Exercises p.783
13-7 Calculations with Maple Exercises p.788
Review Exercises p.788
Challenge Problems p.789

Chapter 14

Multiple Integration

14-1 Double Integrals Exercises p.795
14-2 Iteration of Double Integrals in Cartesian Coordinates Exercises p.802
14-3 Improper Integrals and a Mean-Value Theorem Exercises p.807
14-4 Double Integrals in Polar Coordinates Exercises p.817
14-5 Triple Integrals Exercises p.823
14-6 Change of variables in Triple Integrals Exercises p.830
14-7 Applications of Multiple Integrals Exercises p.838
Review Exercises p.840
Challenge Problems p.841

Chapter 15

Vector Fields

15-1 Vector and Scalar Fields Exercises p.848
15-2 Conservative Fields Exercises p.857
15-3 Line Integrals Exercises p.861
15-4 Line Integrals of Vector Fields Exercises p.869
15-5 Surfaces and Surface Integrals Exercises p.880
15-6 Oriented Surfaces and Flux Integrals Exercises p.886
Review Exercises p.886
Challenge Problems p.887

Chapter 16

Vector Calculus

16-1 Gradient, Divergence, and Curl Exercises p.896
16-2 Some Identities Involving Grad, Div, and Curl Exercises p.902
16-3 Green's Theorem in the Plane Exercises p.906
16-4 The Divergence Theorem in 3-Space Exercises p.912
16-5 Stoke's Theorem Exercises p.916
16-6 Some Physical Applications of Vector Calculus Exercises p.924
16-7 Orthogonal Curvilinear Coordinates Exercises p.934
Review Exercises p.934
Challenge Problems p.935

Chapter 17

Ordinary Differential Equations

17-1 Classifying Differential Equations Exercises p.940
17-2 Solving First-Order Equations Exercises p.945
17-3 Existence, Uniqueness, and Numerical Methods Exercises p.953
17-4 Differential Equations of Second Order Exercises p.957
17-5 Linear Differential Equations with Constant Coefficients Exercises p.961
17-6 Nonhomogeneous Linear Equations Exercises p.967
17-7 Series Solutions of Differential Equations Exercises p.972
Review Exercises p.972

Chapter Appendix I

Complex Numbers

Exercises p.A-10

Chapter Appendix II

Complex Functions

Exercises p.A-19

Chapter Appendix III

Continuous Functions

Exercises p.A-25

Chapter Appendix IV

The Riemann Integral

Exercises p.A-31
Not your book? How about one of these?
Calculus: A Complete Course, 9th Edition
Calculus: A Complete Course, 8th Edition
Calculus: A Complete Course, 6th Edition

Can you find your fundamental truth using Slader as a Calculus: A Complete Course solutions manual?

YES! Now is the time to redefine your true self using Slader’s Calculus: A Complete Course answers. Shed the societal and cultural narratives holding you back and let step-by-step Calculus: A Complete Course textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life. Unlock your Calculus: A Complete Course PDF (Profound Dynamic Fulfillment) today. YOU are the protagonist of your own life. Let Slader cultivate you that you are meant to be!

Good news! We have your answer.

Navigate to your page and exercise.

Remove ads. Upgrade to premium!

Calculus: A Complete Course, 7th Edition


Get it done faster — all your solutions on one page, free of ads.

remove page
add page