


Four Ways to Represent a Function 


2  (9) 


11  (6) 

New Functions from Old Functions 


17  (4) 

Graphing Calculators and Computers 


21  (2) 


23  (4) 

Inverse Functions and Logarithms 


27  (9) 


33  (3) 

Limits and Rates of Change 



The Tangent and Velocity Problems 


36  (3) 


39  (8) 

Calculating Limits Using the Limit Laws 


47  (7) 

The Precise Definition of a Limit 


54  (5) 


59  (4) 

Limits at Infinity; Horizontal Asymptotes 


63  (6) 

Tangents, Velocities, and Other Rates of Change 


69  (3) 


72  (5) 

The Derivative as a Function 


77  (11) 


83  (5) 



Derivatives of Polynomials and Exponential Functions 


88  (3) 

The Product and Quotient Rules 


91  (2) 

Rates of Change in the Natural and Social Sciences 


93  (3) 

Derivatives of Trigonometric Functions 


96  (3) 


99  (4) 


103  (7) 


110  (3) 

Derivatives of Logarithmic Functions 


113  (3) 


116  (4) 


120  (6) 

Linear Approximations and Differentials 


126  (8) 


130  (4) 

Applications of Differentiation 



Maximum and Minimum Values 


134  (6) 


140  (4) 

How Derivatives Affect the Shape of a Graph 


144  (8) 

Indeterminante Forms and L' Hospital's Rule 


152  (4) 

Summary of Curve Sketching 


156  (5) 

Graphing with Calculus and Calculators 


161  (2) 


163  (3) 

Applications to Business and Economics 


166  (2) 


168  (2) 


170  (8) 


173  (5) 




178  (6) 


184  (6) 

The Fundamental Theorem of Calculus 


190  (2) 

Indefinite Integrals and the Net Change Theorem 


192  (4) 


196  (6) 

The Logarithm Defined as an Integral 


202  (8) 


207  (3) 

Applications of Integration 




210  (5) 


215  (4) 

Volumes by Cylindrical Shells 


219  (2) 


221  (2) 

Average Value of a Function 


223  (6) 


226  (3) 

Techniques of Integration 




229  (3) 


232  (4) 

Trigonometric Substitution 


236  (4) 

Integration of Rational Functions by Partial Fractions 


240  (5) 


245  (2) 

Using Tables of Integrals and Computer Algebra Systems 


247  (2) 


249  (5) 


254  (8) 


258  (4) 

Further Applications of Integration 




262  (5) 

Area of a Surface of Revolution 


267  (2) 

Applications to Physics and Engineering 


269  (4) 

Applications to Economics and Biology 


273  (2) 


275  (5) 


278  (2) 



Modeling with Differential Equations 


280  (2) 

Direction Fields and Euler's Method 


282  (3) 


285  (3) 

Exponential Growth and Decay 


288  (3) 


291  (2) 


293  (2) 


295  (5) 


297  (3) 

Parametric Equations and Polar Coordinates 



Curves Defined by Parametric Equations 


300  (4) 

Calculus with Parametric Curves 


304  (6) 


310  (7) 

Areas and Lengths in Polar Coordinates 


317  (3) 


320  (4) 

Conic Section in Polar Coordinates 


324  (6) 


327  (3) 

Infinite Sequences and Series 




330  (5) 


335  (4) 

The Integral Test and Estimates of Sums 


339  (3) 


342  (3) 


345  (3) 

Absolute Convergence and the Ratio and Root Tests 


348  (5) 

Strategy for Testing Series 


353  (2) 


355  (3) 

Representations of Functions as Power Series 


358  (4) 

Taylor and Maclaurin Series 


362  (7) 


369  (2) 

Applications of Taylor Polynomials 


371  (8) 


375  (4) 




379  (6) 


385  (9) 


394  (11) 


405  (11) 


416  (6) 


422  (5) 


427  (8) 


435  (5) 


440  (7) 


447  (6) 


453  (12) 
Answers to On Your Own 

465  