Preliminaries
1 Lines　1
2 Functions and Graphs　1 0
3 Exponential Functions　24
4 Inverse Functions and Logarithms　3 1
5 Trigonometric Functions and Their lnverses 44
6 Parametric Equations　60
7　Modeling Change　67
QUESTIONS TO GUIDE YOUR REVIEW　76
PRACTICE EXERCISES　77
ADDITIONAL EXERCISES：THEORY．EXAMPS．APPUCATIONS 80
1　Limits and Continuity
1．1 Rates of Change and Limi85
1．2 Finding Limiand One-Sided Limits　99
1．3 LimiInvolving Infinity　11 2
1．4 Continuity　123
1．5 Tangent Lines　134
QUESTIONS TO GUIDE YOUR REVIEW　1 41
PRACTICE EXERCISES　1 42
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS　1 43
2 DeriVatives
2．1 The Derivative as a Function　147
2．2 The Derivative as a Rate of Change　1 60
2．3 Derivatives of Products．Quotients．and Negative Powers　173
2．4 Derivatives of Trigonometric Functions　1 79
2．5 The Chain Rule and Parametric Equations　1 87
2．6 Implicit Difierentiation　1 98
2．7 Related Rates　207
QUESTIONS TO GUIDE YOUR REVIEW　21 6
PRACTICE EXERCISES　21 7
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS　221
3 Applications of Derivatives
3．1 Extreme Values of Functions　　225
3．2 The Mcan Value Theorem and Difierential Equations　237
3．3 The Shape of a Graph　245
3．4 Graphical Solutions of Autonomous Differential Equations　257
3．5 Modeling and Optimization　266
3．6 Linearization and Differentials　283
3．7 Newton’S Method　297
QUESTIONS TO GUIDE YOUR REVIEW　305
PRACTICE EXERCISES　305
ADDITIONAL EXERCISES：THEORY，EXAMPLES．APPLICATIONS　309
4 Integration
4．1 Indefinite Integrals，Differential Equations．and Modeling　3 1 3
4．2 Integral Rules；Integration by Substitution　322
4．3 Estimating with Finite Sums　329
4．4 Ricmann Sums and Definite Integrals　340
4．5 The Mcan Value and FundamentaI Theorems　351
4．6 SubStitution in Definite Integrals　364
4．7 NumericalIntegration　373
QUESTIONS TO GUIDE YOUR REVIEW　384
PRACTICE EXERCISES　385
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS　389
5 Applications of Integrals
5．1 Volumes by Slicing and Rotation About an Axis　393
5．2 Modeling Volume Using Cylindrical Shells 406
5．3 Lengths of Plane Curves 41 3
5．4 Springs．Pumping．and Lifting 421
5．5 Fluid Forces 432
5．6 Moments and Centers of Mass 439
QUESTIONS TO GUIDE YOUR REVIEW 451
PRACTICE EXERCISES 45 1
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 454
6 Transcendental Functions and Differential Equations
6．1 Logarithms 457
6．2 Exponential Functions 466
6．3 D——e|rivatives of Inverse Trigonometric Functions；Integrals 477
6．4 First．Order Separable Differential Equations 485
6．5 Linear FirSt．Order Differential Equations 499
6．6 Euler‘S Method；Poplulation Models　507
6．7 Hyperbolic Functions　520
QUESTIONS TO GUIDE YOUR REVIEW　530
PRACTICE EXERCISES　531
ADDmONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS　535
7 Integration Techniques，LH6pital’s Rule，and Improper Integrals
7．1 Basic Integration Formulas　539
7．2 Integration by Parts　546
7．3 Partial Fractions　555
7，4 Trigonometric Substitutions　565
7．5 Integral Tables．Computer Algebra Systems．and
Monte Cario Integration　570
7．6 LHSpitarS Rule　578
7．7 Improper Integrals　586
QUESTIONS TO GUIDE YOUR REVIEW　600
PRACTICE EXERCISES　601
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS　603
8 Infinite Series
8．1 Limis of Sequences of Numbers　608
8．2 Subsequences．Bounded Sequences．and PicardS Method　61 9
8．3 Infinite Series　627
8．4 Series of Nonnegative Terms　1639
8．5 Alternating Series。Absolute and Conditional Convergence　651
8．6 Power Series　660
8．7 Taylor and Maclaurin Series　669
8．8 Applications of Power Series　683
8．9　Fourier Series 691
8．10 Fourier Cosine and Sine Series　698
QUESTIONS TO GUIDE YOUR REVIEW　707
PRACTICE EXERCISES　708
ADDITIONAL EXERCISES：THEORY，EXAMPS．APPLICATIONS　7 11
9 Vectors in the Plane and Polar Functions
9．1 Vectors in the Plane　71 7
9．2 Dot Products　728
9．3 Vector-Valued Functions　738
9．4 Modeling Projectile Motion　749
9．5 Polar Coordinates and Graphs　761
9．6 Calculus of Polar Curyes　770
QUESTIONS TO GUIDE YOUR REVIEW　　780
PRACTICE EXERCISES　780
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS　784
10 Vectors and M0tion in Space
1O．1 Cartesian(Rectangular)Coordinates and Vectors in Space　787
10．2 Dot and Cross Products　796
10．3 Lines and Planes in Space 807
10．4 cylinders and Ouadric SurfaCes 816
10．5 Vector-Valued Functions and Space Curves 825
10．6 Arc Length and the Unit Tangent Vector T 838
10．7 The TNB Frame；Tangential and Normal Components of Acceleration
10．8 Planetary Motion and Satellites 857
QUESTIONS TO GUIDE YOUR REVIEW 866
PRACTICE EXERCISES 867
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 870
11 Multivariable Functions and 111eir Derivatives
1 1．1 Functions of SeveraI Variables 873
11．2 Limits and Continuity in Higher Dimensions 882
11．3 PartiaI Derivatives 890
11．4 The Chain Rule　902
11．5 DirectionaI Derivatives．Gradient Vectors．and Tangent Planes　91 1
11．6 Linearization and Difierentials　925
11．7 Extreme Values and Saddle Points　936
……
12 Multiple Integrals
13 Integration in Vector Fields
Appendices