Chapter 1
Functions And Their Graphs
1 | Functions | Exercises | p.74 |
2 | Analyzing Graphs of Functions | Exercises | p.87 |
3 | Shifting, Reflecting, and Stretching Graphs | Exercises | p.97 |
4 | Combinations of Functions | Exercises | p.106 |
5 | Inverse Functions | Exercises | p.114 |
6 | Mathematical Modeling | Exercises | p.124 |
Review Exercises | p.130 | ||
Problem Solving | p.133 |
Chapter 2
Polynomial And Rational Functions
1 | Quadratic Functions | Exercises | p.142 |
2 | Polynomial Functions of Higher Degree | Exercises | p.154 |
3 | Polynomial and Synthetic Division | Exercises | p.164 |
4 | Complex Numbers | Exercises | p.172 |
5 | The Fundamental Theorem of Algebra | Exercises | p.181 |
6 | Rational Functions | Exercises | p.193 |
Review Exercises | p.198 | ||
Problem Solving | p.201 |
Chapter 3
Limits And Their Properties
1 | A Preview of Calculus | Exercises | p.209 |
2 | Finding Limits Graphically and Numerically | Exercises | p.215 |
3 | Evaluating Limits Analytically | Exercises | p.224 |
4 | Continuity and One-Sided Limits | Exercises | p.234 |
5 | Infinite Limits | Exercises | p.243 |
Review Exercises | p.246 | ||
Problem Solving | p.248 |
Chapter 4
Differentiation
1 | The Derivative and the Tangent Line Problem | Exercises | p.259 |
2 | Basic Differentiation Rules and Rates of Change | Exercises | p.270 |
3 | The Product and Quotient Rules and Higher-Order Derivatives | Exercises | p.280 |
4 | The Chain Rule | Exercises | p.289 |
5 | Implicit Differentiation | Exercises | p.297 |
6 | Related Rates | Exercises | p.304 |
Review Exercises | p.307 | ||
Problem Solving | p.311 |
Chapter 5
Applications Of Differentiation
1 | Extrema on an Interval | Exercises | p.319 |
2 | Rolle's Theorem and the Mean Value Theorem | Exercises | p.326 |
3 | Increasing and Decreasing Functions and the First Derivative Test | Exercises | p.335 |
4 | Concavity and the Second Derivative Test | Exercises | p.343 |
5 | Limits at Infinity | Exercises | p.353 |
6 | A Summary of Curve Sketching | Exercises | p.361 |
7 | Optimization Problems | Exercises | p.369 |
8 | Differentials | Exercises | p.380 |
Review Exercises | p.382 | ||
Problem Solving | p.385 |
Chapter 6
Integration
1 | Antiderivatives and Indefinite Integration | Exercises | p.394 |
2 | Area | Exercises | p.406 |
3 | Riemann Sums and Definite Integrals | Exercises | p.417 |
4 | The Fundamental Theorem of Calculus | Exercises | p.429 |
5 | Integration by Substitution | Exercises | p.442 |
Exercises | p.449 | ||
Review Exercises | p.451 | ||
Problem Solving | p.454 |
Chapter 7
Exponential And Logarithmic Functions
1 | Exponential Functions and Their Graphs | Exercises | p.464 |
2 | Logarithmic Functions and Their Graphs | Exercises | p.475 |
3 | Using Properties of Logarithms | Exercises | p.483 |
4 | Exponential and Logarithmic Equations | Exercises | p.491 |
5 | Exponential and Logarithmic Models | Exercises | p.502 |
Review Exercises | p.507 | ||
Problem Solving | p.511 |
Chapter 8
Exponential And Logarithmic Functions And Calculus
1 | Exponential Functions: Differentiation and Integration | Exercises | p.518 |
2 | Logarithmic Functions and Differentiation | Exercises | p.526 |
3 | Logarithmic Functions and Integration | Exercises | p.535 |
4 | Differential Equations: Growth and Decay | Exercises | p.542 |
Review Exercises | p.544 | ||
Problem Solving | p.546 |
Chapter 9
Trigonometric Functions
1 | Radian and Degree Measure | Exercises | p.556 |
2 | Trigonometric Functions: The Unit Circle | Exercises | p.564 |
3 | Right Triangle Trigonometry | Exercise | p.571 |
4 | Trigonometric Functions of Any Angle | Exercises | p.580 |
5 | Graphs of Sine and Cosine Functions | Exercises | p.590 |
6 | Graphs of Other Trigonometric Functions | Exercises | p.600 |
7 | Inverse Trigonometric Functions | Exercises | p.610 |
8 | Applications and Models | Exercises | p.617 |
Exercises | p.622 | ||
Problem Solving | p.625 |
Chapter 10
Analytic Trigonometry
1 | Using Fundamental Trigonometric Identities | Exercises | p.632 |
2 | Verifying Trigonometric Identities | Exercises | p.639 |
3 | Solving Trigonometric Equations | Exercises | p.647 |
4 | Sum and Difference Formulas | Exercises | p.655 |
5 | Multiple-Angle and Product-to-Sum Formulas | Exercises | p.663 |
Review Exercises | p.667 | ||
Problem Solving | p.669 |
Chapter 11
Trigonometric Functions And Calculus
1 | Limits of Trigonometric Functions | Exercises | p.675 |
2 | Trigonometric Functions: Differentiation | Exercises | p.685 |
3 | Trigonometric Functions: Integration | Exercises | p.694 |
4 | Inverse Trigonometric Functions: Differentiation | Exercises | p.700 |
5 | Inverse Trigonometric Functions: Integration | Exercises | p.707 |
6 | Hyperbolic Functions | Exercises | p.717 |
Exercises | p.719 | ||
Problem Solving | p.722 |
Chapter 12
Topics In Analytic Geometry
1 | Introduction to Conics: Parabolas | Exercises | p.730 |
2 | Ellipses and Implicit Differentiation | Exercises | p.738 |
3 | Hyperbolas and Implicit Differentiation | Exercises | p.747 |
4 | Parametric Equations and Calculus | Exercises | p.755 |
5 | Polar Coordinates and Calculus | Exercises | p.763 |
6 | Graphs of Polar Equations | Exercises | p.768 |
7 | Polar Equations of Conics | Exercises | p.771 |
Exercises | p.775 | ||
Problem Solving | p.778 |
Chapter 13
Additional Topics In Trigonometry
1 | Law of Sines | Exercises | p.788 |
2 | Law of Cosines | Exercises | p.795 |
3 | Vectors in the Plane | Exercises | p.806 |
4 | Vectors and Dot Products | Exercises | p.816 |
5 | Trigonometric Form of a Complex Number | Exercises | p.825 |
Exercises | p.828 | ||
Problem Solving | p.831 |
Chapter 14
Systems Of Equations And Matrices
1 | Systems of Linear Equations in Two Variables | Exercises | p.843 |
2 | Multivariable Linear Systems | Exercises | p.854 |
3 | Systems of Inequalities | Exercises | p.863 |
4 | Matrices and Systems of Equations | Exercises | p.877 |
5 | Operations with Matrices | Exercises | p.890 |
6 | The Inverse of a Square Matrix | Exercises | p.900 |
7 | The Determinant of a Square Matrix | Exercises | p.907 |
Exercises | p.910 | ||
Problem Solving | p.915 |
Chapter P
Prerequisites
1 | Solving Equations | Exercises | p.11 |
2 | Solving Inequalities | Exercises | p.23 |
3 | Graphical Representations of Data | Exercises | p.33 |
4 | Graphs of Equations | Exercises | p.44 |
5 | Linear Equations in Two Variables | Exercises | p.56 |
Review Exercises | p.62 | ||
Problem Solving | p.65 |