

1  (32) 

Four Ways to Represent a Function 


1  (4) 

Mathematical Models: A Catalog of Essential Functions 


5  (3) 

New Functions from Old Functions 


8  (6) 

Graphing Calculators and Computers 


14  (4) 


18  (3) 

Inverse Functions and Logarithms 


21  (12) 


25  (6) 

Principles of Problem Solving 


31  (2) 


33  (44) 

The Tangent and Velocity Problems 


33  (2) 


35  (4) 

Calculating Limits Using the Limit Laws 


39  (4) 

The Precise Definition of a Limit 


43  (3) 


46  (5) 

Limits at Infinity; Horizontal Asymptotes 


51  (7) 

Tangents, Velocities, and Other Rates of Change 


58  (3) 


61  (3) 

The Derivative as a Function 


64  (13) 


69  (6) 


75  (2) 


77  (56) 

Derivatives of Polynomials and Exponential Functions 


77  (4) 

The Product and Quotient Rules 


81  (3) 

Rates of Change in the Natural and Social Sciences 


84  (4) 

Derivatives of Trigonometric Functions 


88  (2) 


90  (5) 


95  (6) 


101  (4) 

Derivatives of Logarithmic Functions 


105  (3) 


108  (3) 


111  (4) 

Linear Approximations and Differentials 


115  (18) 


118  (9) 


127  (6) 

Applications of Differentiation 


133  (88) 

Maximum and Minimum Values 


133  (5) 


138  (3) 

How Derivatives Affect the Shape of a Graph 


141  (11) 

Indeterminate Forms and L'Hospital's Rule 


152  (5) 

Summary of Curve Sketching 


157  (13) 

Graphing with Calculus and Calculators 


170  (10) 


180  (10) 

Applications to Business and Economics 


190  (2) 


192  (5) 


197  (24) 


202  (13) 


215  (6) 


221  (30) 


221  (5) 


226  (5) 

The Fundamental Theorem of Calculus 


231  (4) 

Indefinite Integrals and the Net Change Theorem 


235  (3) 


238  (4) 

The Logarithm Defined as an Integral 


242  (9) 


243  (6) 


249  (2) 

Applications of Integration 


251  (32) 


251  (7) 


258  (8) 

Volumes by Cylindrical Shells 


266  (5) 


271  (2) 

Average Value of a Function 


273  (10) 


274  (5) 


279  (4) 

Techniques of Integration 


283  (56) 


283  (4) 


287  (4) 

Trigonometric Substitution 


291  (5) 

Integration of Rational Functions by Partial Fractions 


296  (7) 


303  (5) 

Integration Using Tables and Computer Algebra Systems 


308  (4) 


312  (7) 


319  (20) 


326  (9) 


335  (4) 

Further Applications of Integration 


339  (26) 


339  (3) 

Area of a Surface of Revolution 


342  (4) 

Applications to Physics and Engineering 


346  (7) 

Applications to Economics and Biology 


353  (2) 


355  (10) 


357  (4) 


361  (4) 


365  (32) 

Modeling with Differential Equations 


365  (1) 

Direction Fields and Euler's Method 


366  (4) 


370  (5) 

Exponential Growth and Decay 


375  (2) 


377  (4) 


381  (4) 


385  (12) 


387  (6) 


393  (4) 

Parametric Equations and Polar Coordinates 


397  (46) 

Curves Defined by Parametric Equations 


397  (5) 

Calculus with Parametric Curves 


402  (8) 


410  (9) 

Areas and Lengths in Polar Coordinates 


419  (7) 


426  (4) 

Conic Sections in Polar Coordinates 


430  (13) 


433  (8) 


441  (2) 

Infinite Sequences and Series 


443  (78) 


443  (5) 


448  (6) 

The Integral Test and Estimates of Sums 


454  (4) 


458  (2) 


460  (3) 

Absolute Convergence and the Ratio and Root Tests 


463  (3) 

Strategy for Testing Series 


466  (2) 


468  (3) 

Representations of Functions as Power Series 


471  (5) 

Taylor and Maclaurin Series 


476  (7) 


483  (4) 

Applications of Taylor Polynomials 


487  (20) 


494  (7) 


501  (6) 



A Numbers, Inequalities, and Absolute Values 


507  (2) 

B Coordinate Geometry and Lines 


509  (3) 

C Graphs of SecondDegree Equations 


512  (2) 


514  (5) 


519  (2) 


521  