What textbook chapter and section from Calculus: Early Transcendentals can I use to learn this content: 
Estimate the limit at a given point given a graph or table of data. (From part 1 of the course)	
61.1.2	
14%	Apply the properties of limits. (From part 1 of the course)	
61.1.3	
14%	Calculate and interpret limits involving infinity. (From part 1 of the course)	
61.1.4	
14%	Understand continuity in terms of limits. (From part 1 of the course)	
61.1.5	
Calculate and interpret the average and instantaneous rates of change. (From part 1 of the course)	
61.2.1	
Understand and apply the definition of the derivative. (From part 1 of the course)	
61.2.2	
14%	Understand the relationship between differentiability and continuity and recognize the graph of f’ from the graph of f. (From part 1 of the course)	
61.2.3	
14%	Understand and apply the rules for differentiating power functions. (From part 1 of the course)	
61.2.4	
14%	Understand and apply the rules for differentiating trigonometric functions. (From part 1 of the course)	
61.2.5	
14%	Use the chain rule to find the derivative of composite functions. (From part 1 of the course)	
Unit 2 Quiz | Multiple-Choice Section (You must complete before continuing) | Multiple-Choice Section (You must complete before continuing) | Lesson 5 - The Chain Rule | CK-12 Textbook	
61.3.1	
14%	Understand and calculate the derivative of exponential and logarithmic functions. (From part 1 of the course)	
61.3.2	
14%	Calculate the derivative of inverse trigonometric functions. (From part 1 of the course)	
61.3.3	
12%	Understand and use implicit differentiation. (From part 1 of the course)	
61.3.4	
12%	Use implicit differentiation to find the derivative of inverse functions. (From part 1 of the course)	
61.4.1	
12%	Understand what critical points are and how they can be used to analyze the curve of a function. (From part 1 of the course)	
61.4.2	
12%	Understand what points of inflection are and how they can be used to analyze the curve of a function. (From part 1 of the course)	
61.4.3	
12%	Understand what extrema are and find them using the first and second derivatives. (From part 1 of the course)	
61.4.4	
Understand and apply the mean value theorem. (From part 1 of the course)	
61.5.1	
Solve problems dealing with maxima and minima. (From part 1 of the course)	
61.5.2	
13%	Use the derivative to solve questions related to distance, velocity, acceleration, and rectilinear motion. (From part 1 of the course)	
61.5.3	
13%	Use the derivative to solve problems with related rates. (From part 1 of the course)	
61.5.4	
14%	Use l&#39;Hopital&#39;s rule to solve indeterminate limits. (From part 1 of the course)	
63.1.1	
50%	Approximate the area of almost any shape by splitting the shape into small sections.	
63.1.2	
100%	Understand that the definite integral is an efficient way to write Riemann sums. Evaluate definite integrals using geometry.	
63.1.3	
64%	Understand the relationship between derivatives and definite integrals.	
63.1.4	
66%	Use the Fundamental Theorem of Calculus to evaluate definite integrals.	
63.1.5	
19%	Use the Trapezoidal Rule to approximate the value of definite integrals and to approximate the area under a curve.	
63.1.6	
100%	Interpret average and instantaneous rates of change	
63.2.1	
67%	Understand five properties of definite integrals.	
63.2.2	
65%	Understand how antiderivatives are related to indefinite integrals. Find antiderivatives for some basic integrals.	
63.2.3	
75%	Find antiderivatives for expressions that are the result of the chain rule in differentiation.	
63.2.4	
48%	Use the skills of integration to evaluate definite integrals.	
63.3.1	
75%	Set up and evaluate integrals to find areas.	
63.3.2	
100%	Set up and evaluate integrals to find volumes for solids of revolution.	
63.3.3	
66%	Set up and evaluate integrals for volumes of solids of any cross section.	
63.3.4	
74%	Use integration to calculate the average value of a function and analyze motion.	
63.4.1	
82%	Understand what differential equations are and how to solve them. Apply them to authentic situations.	
63.4.2	
100%	Set up and solve differential equations to model exponential growth and decay.	
63.4.3	
70%	Approximate solutions to differential equations with slope fields and Euler&#39;s Method.	
63.4.4	
68%	Use the tangent line to approximate values for a function.	
63.5.1	
66%	Deepen understanding of the relationship between the graphs of f(x), f &#39;(x) and f &#39;&#39;(x).	
63.5.2	
66%	Review concepts of integration through authentic data on rates of change.	
63.5.3	
70%	Review concepts of differentiation and the Fundamental Theorem of Calculus by analyzing functions defined by integrals.
TOC:
iii
Preface xi
To the Student xxiii
Diagnostic Tests xxiv
A PREVIEW OF CALCULUS 1
1.1 Four Ways to Represent a Function 10
1.2 Mathematical Models: A Catalog of Essential Functions 23
1.3 New Functions from Old Functions 36
1.4 Graphing Calculators and Computers 44
1.5 Exponential Functions 51
1.6 Inverse Functions and Logarithms 58
Review 72
Principles of Problem Solving 75
2.1 The Tangent and Velocity Problems 82
2.2 The Limit of a Function 87
2.3 Calculating Limits Using the Limit Laws 99
2.4 The Precise Definition of a Limit 108
2.5 Continuity 118
2.6 Limits at Infinity; Horizontal Asymptotes 130
2.7 Derivatives and Rates of Change 143
Writing Project N Early Methods for Finding Tangents 153
2.8 The Derivative as a Function 154
Review 165
Problems Plus 170
1 Functions and Models        9
2 Limits and Derivatives        81
Contents
iv CONTENTS
3.1 Derivatives of Polynomials and Exponential Functions 174
Applied Project N Building a Better Roller Coaster 184
3.2 The Product and Quotient Rules 184
3.3 Derivatives of Trigonometric Functions 191
3.4 The Chain Rule 198
Applied Project N Where Should a Pilot Start Descent? 208
3.5 Implicit Differentiation 209
Laboratory Project N Families of Implicit Curves 217
3.6 Derivatives of Logarithmic Functions 218
3.7 Rates of Change in the Natural and Social Sciences 224
3.8 Exponential Growth and Decay 237
3.9 Related Rates 244
3.10 Linear Approximations and Differentials 250
Laboratory Project N Taylor Polynomials 256
3.11 Hyperbolic Functions 257
Review 264
Problems Plus 268
4.1 Maximum and Minimum Values 274
Applied Project N The Calculus of Rainbows 282
4.2 The Mean Value Theorem 284
4.3 How Derivatives Affect the Shape of a Graph 290
4.4 Indeterminate Forms and l’Hospital’s Rule 301
Writing Project N The Origins of l’Hospital’s Rule 310
4.5 Summary of Curve Sketching 310
4.6 Graphing with Calculus and Calculators 318
4.7 Optimization Problems 325
Applied Project N The Shape of a Can 337
4.8 Newton’s Method 338
4.9 Antiderivatives 344
Review 351
Problems Plus 355
3 Differentiation Rules        173
4 Applications of Differentiation        273
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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
CONTENTS v
5.1 Areas and Distances 360
5.2 The Definite Integral 371
Discovery Project N Area Functions 385
5.3 The Fundamental Theorem of Calculus 386
5.4 Indefinite Integrals and the Net Change Theorem 397
Writing Project N Newton, Leibniz, and the Invention of Calculus 406
5.5 The Substitution Rule 407
Review 415
Problems Plus 419
6.1 Areas Between Curves 422
Applied Project N The Gini Index 429
6.2 Volumes 430
6.3 Volumes by Cylindrical Shells 441
6.4 Work 446
6.5 Average Value of a Function 451
Applied Project N Calculus and Baseball 455
Applied Project N Where to Sit at the Movies 456
Review 457
Problems Plus 459
7.1 Integration by Parts 464
7.2 Trigonometric Integrals 471
7.3 Trigonometric Substitution 478
7.4 Integration of Rational Functions by Partial Fractions 484
7.5 Strategy for Integration 494
7.6 Integration Using Tables and Computer Algebra Systems 500
Discovery Project N Patterns in Integrals 505
5 Integrals        359
6 Applications of Integration        421
7 Techniques of Integration        463
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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
vi CONTENTS
7.7 Approximate Integration 506
7.8 Improper Integrals 519
Review 529
Problems Plus 533
8.1 Arc Length 538
Discovery Project N Arc Length Contest 545
8.2 Area of a Surface of Revolution 545
Discovery Project N Rotating on a Slant 551
8.3 Applications to Physics and Engineering 552
Discovery Project N Complementary Coffee Cups 562
8.4 Applications to Economics and Biology 563
8.5 Probability 568
Review 575
Problems Plus 577
9.1 Modeling with Differential Equations 580
9.2 Direction Fields and Euler’s Method 585
9.3 Separable Equations 594
Applied Project N How Fast Does a Tank Drain? 603
Applied Project N Which Is Faster, Going Up or Coming Down? 604
9.4 Models for Population Growth 605
9.5 Linear Equations 616
9.6 Predator-Prey Systems 622
Review 629
Problems Plus 633
8 Further Applications of Integration        537
9 Differential Equations        579
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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
CONTENTS vii
10.1 Curves Defined by Parametric Equations 636
Laboratory Project N Running Circles around Circles 644
10.2 Calculus with Parametric Curves 645
Laboratory Project N Bézier Curves 653
10.3 Polar Coordinates 654
Laboratory Project N Families of Polar Curves 664
10.4 Areas and Lengths in Polar Coordinates 665
10.5 Conic Sections 670
10.6 Conic Sections in Polar Coordinates 678
Review 685
Problems Plus 688
11.1 Sequences 690
Laboratory Project N Logistic Sequences 703
11.2 Series 703
11.3 The Integral Test and Estimates of Sums 714
11.4 The Comparison Tests 722
11.5 Alternating Series 727
11.6 Absolute Convergence and the Ratio and Root Tests 732
11.7 Strategy for Testing Series 739
11.8 Power Series 741
11.9 Representations of Functions as Power Series 746
11.10 Taylor and Maclaurin Series 753
Laboratory Project N An Elusive Limit 767
Writing Project N How Newton Discovered the Binomial Series 767
11.11 Applications of Taylor Polynomials 768
Applied Project N Radiation from the Stars 777
Review 778
Problems Plus 781
10 Parametric Equations and Polar Coordinates        635
11 Infinite Sequences and Series        689
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
viii CONTENTS
12.1 Three-Dimensional Coordinate Systems 786
12.2 Vectors 791
12.3 The Dot Product 800
12.4 The Cross Product 808
Discovery Project N The Geometry of a Tetrahedron 816
12.5 Equations of Lines and Planes 816
Laboratory Project N Putting 3D in Perspective 826
12.6 Cylinders and Quadric Surfaces 827
Review 834
Problems Plus 837
13.1 Vector Functions and Space Curves 840
13.2 Derivatives and Integrals of Vector Functions 847
13.3 Arc Length and Curvature 853
13.4 Motion in Space: Velocity and Acceleration 862
Applied Project N Kepler’s Laws 872
Review 873
Problems Plus 876
14.1 Functions of Several Variables 878
14.2 Limits and Continuity 892
14.3 Partial Derivatives 900
14.4 Tangent Planes and Linear Approximations 915
14.5 The Chain Rule 924
14.6 Directional Derivatives and the Gradient Vector 933
14.7 Maximum and Minimum Values 946
Applied Project N Designing a Dumpster 956
Discovery Project N Quadratic Approximations and Critical Points 956
12 Vectors and the Geometry of Space        785
13 Vector Functions        839
14 Partial Derivatives        877
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
CONTENTS ix
14.8 Lagrange Multipliers 957
Applied Project N Rocket Science 964
Applied Project N Hydro-Turbine Optimization 966
Review 967
Problems Plus 971
15.1 Double Integrals over Rectangles 974
15.2 Iterated Integrals 982
15.3 Double Integrals over General Regions 988
15.4 Double Integrals in Polar Coordinates 997
15.5 Applications of Double Integrals 1003
15.6 Surface Area 1013
15.7 Triple Integrals 1017
Discovery Project N Volumes of Hyperspheres 1027
15.8 Triple Integrals in Cylindrical Coordinates 1027
Discovery Project N The Intersection of Three Cylinders 1032
15.9 Triple Integrals in Spherical Coordinates 1033
Applied Project N Roller Derby 1039
15.10 Change of Variables in Multiple Integrals 1040
Review 1049
Problems Plus 1053
16.1 Vector Fields 1056
16.2 Line Integrals 1063
16.3 The Fundamental Theorem for Line Integrals 1075
16.4 Green’s Theorem 1084
16.5 Curl and Divergence 1091
16.6 Parametric Surfaces and Their Areas 1099
16.7 Surface Integrals 1110
16.8 Stokes’ Theorem 1122
Writing Project N Three Men and Two Theorems 1128
15 Multiple Integrals        973
16 Vector Calculus        1055
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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
x CONTENTS
16.9 The Divergence Theorem 1128
16.10 Summary 1135
Review 1136
Problems Plus 1139
17.1 Second-Order Linear Equations 1142
17.2 Nonhomogeneous Linear Equations 1148
17.3 Applications of Second-Order Differential Equations 1156
17.4 Series Solutions 1164
Review 1169
A Numbers, Inequalities, and Absolute Values A2
B Coordinate Geometry and Lines A10
C Graphs of Second-Degree Equations A16
D Trigonometry A24
E Sigma Notation A34
F Proofs of Theorems A39
G The Logarithm Defined as an Integral A50
H Complex Numbers A57
I Answers to Odd-Numbered Exercises A65
17 Second-Order Differential Equations        1141