

1  (222) 




8  (2) 

Linear Models and Rates of Change 


10  (2) 

Functions and Their Graphs 


12  (2) 


14  (3) 


14  (3) 

Limits and Their Properties 




17  (1) 

Finding Limits Graphically and Numerically 


17  (1) 

Evaluating Limits Analytically 


18  (2) 

Continuity and OneSided Limits 


20  (3) 


23  (4) 


25  (2) 



The Derivative and the Tangent Line Problem 


27  (2) 

Basic Differentiation Rules and Rates of Change 


29  (3) 

The Product and Quotient Rules and HigherOrder Derivatives 


32  (2) 


34  (2) 


36  (3) 


39  (8) 


43  (4) 

Applications of Differentiation 




47  (32) 

Rolle's Theorem and the Mean Value Theorem 


79  

Increasing and Decreasing Functions and the First Derivative Test 


51  (34) 

Concavity and the Second Derivative Test 


85  


56  (2) 

A Summary of Curve Sketching 


58  (3) 


61  (4) 


65  (1) 


66  (1) 

Business and Economic Applications 


67  (9) 


69  (7) 



Antiderivatives and Indefinite Integration 


76  (2) 


78  (2) 

Riemann Sums and Definite Integrals 


80  (743) 

The Fundamental Theorem of Calculus 


823  

Integration by Substitution 


84  (5) 


89  (5) 


91  (3) 

Logarithmic, Exponential, and Other Transcendental Functions 



The Natural Logarithmic Function and Differentiation 


94  (2) 

The Natural Logarithmic Function and Integration 


96  (2) 


98  (2) 

Exponential Functions: Differentiation and Integration 


100  (3) 

Bases Other than e and Applications 


103  (1) 

Differential Equations: Growth and Decay 


104  (2) 

Differential Equations; Separation of Variables 


106  (4) 

Inverse Trigonometric Functions and differentiation 


110  (1) 

Inverse Trigonometric Functions and Integration 


111  (2) 


113  (5) 


115  (3) 

Applications of Integration 



Area of a Region Between Two Curves 


118  (2) 


120  (4) 


124  (3) 

Arc Length and Surfaces of Revolution 


127  (2) 


129  (2) 

Moments, Centers and Mass, and Centroids 


131  (3) 

Fluid Pressure and Fluid Force 


134  (5) 


134  (5) 

Integration Techniques, L'Hopital's Rule, and Improper Integrals 




139  (2) 


141  (5) 


146  (3) 

Trigonometric Substitution 


149  (5) 


154  (2) 

Integration by Tables and Other Integration Techniques 


156  (2) 

Indeterminate Forms and L'Hopital's Rule 


158  (2) 


160  (8) 


163  (5) 




168  (2) 


170  (2) 

The Integral Test and pseries 


172  (1) 


173  (1) 


174  (2) 


176  (2) 

Taylor Polynomials and Approximations 


178  (3) 


181  (2) 

Representation of Functions by Power Series 


183  (2) 

Taylor and Maclaurin Series 


185  (6) 


188  (3) 

Conics, Parametric Equations, and Polar Coordinates 




191  (7) 

Plane Curves and Parametric Equations 


198  (3) 

Parametric Equations and Calculus 


201  (3) 

Area and Arc Length in Polar Coordinates 


204  (3) 

Polar Coordinates and Polar Coordinates 


207  (3) 

Polar Equations of Conics and Kepler's Laws 


210  (2) 


212  (5) 
Appendices 



217  (1) 


218  (2) 


220  (2) 


222  