Introduction 

vii  

1 Equations, Functions, and Graphs 


1  (16) 


1  (1) 


2  (6) 


8  (5) 

1.4 Summary of Main Points 


13  (1) 


14  (3) 

2 Change, and the Idea of the Derivative 


17  (30) 

2.1 Average Rates of Change 


17  (6) 

2.2 Instantaneous Rates of Change 


23  (10) 


33  (4) 

2.4 The Geometric Meaning of Derivatives 


37  (6) 

2.5 Summary of Main Points 


43  (1) 


44  (3) 


47  (22) 


47  (3) 

3.2 Some Complications with the Definition of Limits 


50  (2) 

3.3 The Problem of Division By Zero 


52  (4) 


56  (3) 

3.5 Continuity and Differentiability 


59  (4) 

3.6 Summary of Main Points 


63  (2) 


65  (4) 

4 Computing Some Derivatives 


69  (14) 


70  (3) 

4.2 Fractional Expressions with the Variable in the Denominator 


73  (6) 


79  (1) 


80  (2) 

4.5 Summary of Main Points 


82  (1) 


82  (1) 

5 Formulas for Derivatives 


83  (20) 

5.1 Derivatives of Some Particular Functions 


84  (2) 

5.2 Derivatives of Combinations of Functions 


86  (7) 


93  (8) 

5.4 Summary of Main Points 


101  (1) 


101  (2) 

6 Extreme Values, the Mean Value Theorem, and Curve Sketching 


103  (22) 


104  (6) 

6.2 The Mean Value Theorem 


110  (4) 


114  (7) 

6.4 Summary of Main Points 


121  (1) 


122  (3) 


125  (30) 


125  (6) 

7.2 MaxMin Word Problems 


131  (9) 

7.3 Related Rate Word Problems 


140  (9) 

7.4 Summary of Main Points 


149  (1) 


150  (5) 

8 The Idea of the Integral 


155  (34) 


155  (9) 

8.2 Terminology and Notation 


164  (16) 

8.3 The Definite Integral: Definition and Notation 


180  (3) 

8.4 Summary of Main Points 


183  (2) 


185  (4) 

9 Computing Some Integrals 


189  (18) 

9.1 Summation Rules and Formulas 


189  (10) 

9.2 Computing Limits of Approximate Sums 


199  (3) 

9.3 Summary of Main Points 


202  (2) 


204  (3) 

10 Formulas for Integrals: Integrals, Antiderivatives and the Fundamental Theorem of Calculus 


207  (28) 


207  (1) 

10.2 The Fundamental Theorem of CalculusThe Main Idea 


207  (6) 

10.3 The Fundamental Theorem of CalculusAn Idea of the Proof 


213  (3) 

10.4 Computing Some Antiderivatives 


216  (8) 

10.5 Antiderivatives Involving the Chain Rule 


224  (6) 

10.6 Summary of Main Points 


230  (2) 


232  (3) 

11 Geometric Applications of the Integral 


235  (58) 

11.1 Horizontal vs. Vertical, x vs. y 


235  (8) 


243  (17) 

11.3 Volumes of Solids of RevolutionThe Method of Crosssectional Areas 


260  (15) 

11.4 Volumes of Solids of RevolutionThe Method of Cylindrical Shells 


275  (13) 

11.5 Summary of Main Points 


288  (2) 


290  (3) 


293  (12) 

12.1 Simple Initial Value Problems 


293  (2) 

12.2 Motion with Constant Acceleration 


295  (5) 

12.3 Summary of Main Points 


300  (1) 


301  (4) 
APPENDICES 

305  (17) 
A The Trigonometric Functions 

305  (10) 
A.1 Definitions 

305  (3) 
A.2 Identities 

308  (1) 
A.3 Derivatives 

309  (2) 
A.4 Antiderivatives 

311  (4) 
B Exponential and Logarithmic Functions 

315  (7) 
B.1 Definitions 

315  (1) 
B.2 Identities 

316  (1) 
B.3 Derivatives 

317  (2) 
B.4 Antiderivatives 

319  (3) 
Answers to Exercises 

322  (14) 
Glossary 

336  (3) 
Index 

339  