


Four Ways to Represent a Function 


2  (7) 


9  (6) 

New Functions from Old Functions 


15  (4) 

Graphing Calculators and Computers 


19  (2) 


21  (4) 

Inverse Functions and Logarithms 


25  (9) 


31  (3) 

Limits and Rates of Change 



The Tangent and Velocity Problems 


34  (3) 


37  (8) 

Calculating Limits Using the Limit Laws 


45  (7) 

The Precise Definition of a Limit 


52  (5) 


57  (4) 

Limits at Infinity; Horizontal Asymptotes 


61  (6) 

Tangents, Velocities, and Other Rates of Change 


67  (3) 


70  (5) 

The Derivative as a Function 


75  (11) 


81  (5) 



Derivatives of Polynomials and Exponential Functions 


86  (3) 

The Product and Quotient Rules 


89  (2) 

Rates of Change in the Natural and Social Sciences 


91  (3) 

Derivatives of Trigonometric Functions 


94  (3) 


97  (4) 


101  (7) 


108  (3) 

Derivatives of Logarithmic Functions 


111  (3) 


114  (4) 


118  (5) 

Linear Approximations and Differentials 


123  (7) 


126  (4) 

Applications of Differentiation 



Maximum and Minimum Values 


130  (6) 


136  (4) 

How Derivatives Affect the Shape of a Graph 


140  (8) 

Indeterminante Forms and L'Hospital's Rule 


148  (4) 

Summary of Curve Sketching 


152  (5) 

Graphing with Calculus and Calculators 


157  (2) 


159  (3) 

Applications to Economics 


162  (2) 


164  (2) 


166  (8) 


169  (5) 




174  (6) 


180  (6) 

The Fundamental Theorem of Calculus 


186  (2) 

Indefinite Integrals and the Total Change Theorem 


188  (4) 


192  (6) 

The Logarithm Defined as an Integral 


198  (8) 


203  (3) 

Applications of Integration 




206  (5) 


211  (4) 

Volumes by Cylindrical Shells 


215  (2) 


217  (2) 

Average Value of a Function 


219  (6) 


222  (3) 

Techniques of Integration 




225  (3) 


228  (4) 

Trigonometric Substitution 


232  (4) 

Integration of Rational Functions by Partial Fractions 


236  (5) 


241  (2) 

Using Tables of Integrals and Computer Algebra Systems 


243  (2) 


245  (5) 


250  (8) 


254  (4) 

Further Applications of Integration 




258  (5) 

Area of a Surface of Revolution 


263  (2) 

Applications to Physics and Engineering 


265  (4) 

Applications to Economics and Biology 


269  (2) 


271  (5) 


274  (2) 



Modeling with Differential Equations 


276  (2) 

Direction Fields and Euler's Method 


278  (3) 


281  (3) 

Exponential Growth and Decay 


284  (3) 


287  (2) 


289  (2) 


291  (5) 


293  (3) 

Parametric Equations and Polar Coordinates 



Curves Defined by Parametric Equations 


296  (4) 


300  (4) 

Arc Length and Surface Area 


304  (3) 


307  (7) 

Areas and Lengths in Polar Coordinates 


314  (3) 


317  (4) 

Conic Sections in Polar Coordinates 


321  (7) 


324  (4) 

Infinite Sequences and Series 




328  (5) 


333  (4) 

The Integral Test and Estimates of Sums 


337  (3) 


340  (3) 


343  (3) 

Absolute Convergence and the Ratio and Root Tests 


346  (5) 

Strategy for Testing Series 


351  (2) 


353  (3) 

Representations of Functions as Power Series 


356  (4) 

Taylor and Maclaurin Series 


360  (7) 


367  (2) 

Applications of Taylor Polynomials 


369  (8) 


373  (4) 
On Your Own 



377  (6) 


383  (9) 


392  (11) 


403  (11) 


414  (6) 


420  (5) 


425  (8) 


433  (5) 


438  (7) 


445  (7) 


452  (12) 
Answers to On Your Own 

464  