Preface 

ix  
Introduction 

1  (2) 


3  (67) 

Functions and Their Graphs 


3  (15) 


18  (9) 


27  (7) 

Zeros of FunctionsThe Quadratic Formula and Factoring 


34  (8) 

Exponents and Power Functions 


42  (7) 

Functions and Graphs in Applications 


49  (21) 

Graphing Functions Using Technology 


62  (6) 


68  (2) 


70  (74) 

The Slope of a Straight Line 


72  (11) 

The Slope of a Curve at a Point 


83  (6) 


89  (12) 

Limits and the Derivative 


101  (10) 

Differentiability and Continuity 


111  (5) 

Some Rules for Differentiation 


116  (7) 


123  (5) 

The Derivative as a Rate of Change 


128  (16) 


143  (1) 

Applications of the Derivative 


144  (70) 

Describing Graphs of Functions 


144  (12) 

The First and Second Derivative Rules 


156  (10) 

Curve Sketching (Introduction) 


166  (7) 

Curve Sketching (Conclusion) 


173  (7) 


180  (9) 

Further Optimization Problems 


189  (9) 

Applications of Derivatives to Business and Economics 


198  (16) 


213  (1) 

Techniques of Differentiation 


214  (29) 

The Product and Quotient Rules 


214  (8) 

The Chain Rule and the General Power Rule 


222  (6) 

Implicit Differentiation and Related Rates 


228  (15) 


242  (1) 

The Exponential and Natural Logarithm Functions 


243  (31) 


243  (4) 

The Exponential Function ex 


247  (5) 

Differentiation of Exponential Functions 


252  (5) 

The Natural Logarithm Function 


257  (5) 


262  (4) 

Properties of the Natural Logarithm Function 


266  (8) 


272  (2) 

Applications of the Exponential and Natural Logarithm Functions 


274  (39) 

Exponential Growth and Decay 


274  (10) 


284  (8) 

Applications of the Natural Logarithm Function to Economics 


292  (6) 

Further Exponential Models 


298  (15) 


312  (1) 


313  (54) 


314  (9) 


323  (9) 

Definite Integrals and the Fundamental Theorem 


332  (12) 


344  (10) 

Applications of the Definite Integral 


354  (13) 


366  (1) 

Functions of Several Variables 


367  (63) 

Examples of Functions of Several Variables 


367  (7) 


374  (9) 

Maxima and Minima of Functions of Several Variables 


383  (8) 

Lagrange Multipliers and Constrained Optimization 


391  (11) 

The Method of Least Squares 


402  (7) 


409  (12) 


421  (9) 


429  (1) 

The Trigonometric Functions 


430  (30) 


430  (4) 


434  (8) 

Differentiation and Integration of sin t and cos t 


442  (10) 

The Tangent and Other Trigonometric Functions 


452  (8) 


459  (1) 

Techniques of Integration 


460  (43) 

Integration by Substitution 


461  (7) 


468  (4) 

Evaluation of Definite Integrals 


472  (5) 

Approximation of Definite Integrals 


477  (11) 

Some Applications of the Integral 


488  (5) 


493  (10) 


502  (1) 


503  (45) 

Solutions of Differential Equations 


503  (7) 


510  (9) 

Numerical Solution of Differential Equations 


519  (6) 

Graphing Solutions of Differential Equations 


525  (10) 

Applications of Differential Equations 


535  (13) 


547  (1) 

Taylor Polynomials and Infinite Series 


548  (45) 


548  (8) 

The NewtonRaphson Algorithm 


556  (9) 


565  (10) 

Series with Positive Terms 


575  (6) 


581  (12) 


592  (1) 


593  (46) 

Discrete Random Variables 


593  (8) 

Continuous Random Variables 


601  (9) 

Expected Value and Variance 


610  (6) 

Exponential and Normal Random Variables 


616  (10) 

Poisson and Geometric Random Variables 


626  (13) 


639  
Appendix A: Calculus and the TI82 Calculator 

1  
Appendix B: Calculus and the TI83/TI83 Plus Calculators 

6  
Appendix C: Calculus and the TI85 Calculator 

11  
Appendix D: Calculus and the TI86 Calculator 

16  
Appendix E: Areas under the Standard Normal Curve 

22  
Answers to Exercises 

23  
Index 

1  