


Four Ways to Represent a Function 


2  (9) 


11  (6) 

New Functions from Old Function 


17  (4) 

Graphing Calculators and Computers 


21  (5) 

Technology Plus for Chapter 1 


23  (3) 

Limits and Rates of Change 



The Tangent and Velocity Problems 


26  (3) 


29  (8) 

Calculating Limits Using the Limit Laws 


37  (7) 

The Precise Definition of a Limit 


44  (5) 


49  (4) 

Tangents, Velocities, and Other Rates of Change 


53  (7) 

Technology Plus for Chapter 2 


56  (4) 




60  (5) 

The Derivative as a Function 


65  (6) 


71  (3) 

Rates of Change in the Natural and Social Sciences 


74  (3) 

Derivatives of Trigonometric Functions 


77  (3) 


80  (3) 


83  (4) 


87  (3) 


90  (6) 

Linear Approximations and Differentials 


96  (8) 

Technology Plus for Chapter 3 


100  (4) 

Applications of Differentiation 



Maximum and Minimum Values 


104  (6) 


110  (4) 

How Derivatives Affect the Shape of a Graph 


114  (8) 

Limits at Infinity; Horizontal Asymptotes 


122  (5) 

Summary of a Curve Sketching 


127  (6) 

Graphing with Calculus and Calculators 


133  (2) 


135  (3) 

Applications to Economics 


138  (2) 


140  (2) 


142  (7) 

Technology Plus for Chapter 4 


144  (5) 




149  (5) 


154  (6) 

The Fundamental Theorem of Calculus 


160  (2) 

Indefinite Integrals and the Net Change Theorem 


162  (3) 


165  (7) 

Technology Plus for Chapter 5 


169  (3) 

Applications of Integration 




172  (5) 


177  (4) 

Volumes by Cylindrical Shells 


181  (2) 


183  (2) 

Average Value of a Function Review 


185  (6) 

Technology Plus for Chapter 6 


188  (3) 

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 




191  (4) 

Exponential Functions and Their Derivatives 


195  (5) 


200  (3) 

Derivatives of Logarithmic Functions 


203  (4) 

The Natural Logarithmic Function 


207  (6) 

The Natural Exponential Function 


213  (2) 

General Logarithmic and Exponential Functions 


215  (5) 

Inverse Trigonometric Functions 


220  (5) 


225  (5) 

Indeterminate Forms and L'Hospital's Rule 


230  (7) 

Technology Plus for Chapter 7 


234  (3) 

Techniques of Integration 




237  (3) 


240  (4) 

Trigonometric Substitution 


244  (4) 

Integration of Rational Functions by Partial Fractions 


248  (5) 


253  (2) 

Using Tables of Integrals and Computer Algebra Systems 


255  (2) 


257  (5) 


262  (8) 

Technology Plus for Chapter 8 


266  (4) 

Further Applications of Integration 




270  (5) 

Area of a Surface of Revolution 


275  (2) 

Applications to Physics and Engineering 


277  (4) 

Applications to Economics and Biology 


281  (2) 


283  (5) 

Technology Plus for Chapter 9 


286  (2) 



Modeling with Differential Equations 


288  (2) 

Direction Fields and Euler's Method 


290  (3) 


293  (3) 

Exponential Growth and Decay 


296  (3) 


299  (2) 


301  (2) 


303  (5) 

Technology Plus for Chapter 10 


305  (3) 

Parametric Equations and Polar Coordinates 



Curves Defined by Parametric Equations 


308  (4) 

Calculus with Parametric Curves 


312  (6) 


318  (7) 

Areas and Lengths in Polar Coordinates 


325  (3) 


328  (4) 

Conic Sections in Polar Coordinates 


332  (6) 

Technology Plus for Chapter 11 


335  (3) 

Infinite Sequences and Series 




338  (5) 


343  (4) 

The Integral Test and Estimates of Sums 


347  (3) 


350  (3) 


353  (3) 

Absolute Convergence and the Ratio and Root Tests 


356  (5) 

Strategy for Testing Series 


361  (2) 


363  (3) 

Representations of Functions as Power Series 


366  (4) 

Taylor and Maclaurin Series 


370  (7) 


377  (2) 

Applications of Taylor Polynomials 


379  (8) 

Technology Plus for Chapter 12 


383  (4) 




387  (4) 


391  (6) 


397  (10) 


407  (11) 


418  (5) 


423  (5) 


428  (12) 


440  (8) 


448  (5) 


453  (7) 


460  (6) 


466  (12) 
Answers to On Your Own 

478  