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Functions And Limits
1.1 | Functions and Their Representations | Exercises | p.8 |
1.2 | A Catalog of Essential Functions | Exercises | p.21 |
1.3 | The Limit of a Function | Exercises | p.33 |
1.4 | Calculating Limits | Exercises | p.43 |
1.5 | Continuity | Exercises | p.54 |
1.6 | Limits Involving Infinity | Exercises | p.67 |
Chapter 1 Review (Concept Check) | p.70 | ||
Chapter 1 Review (True-False Quiz) | p.70 | ||
Chapter 1 Review (Exercises) | p.71 |
Derivatives
2.1 | Derivatives and Rates of Change | Exercises | p.80 |
2.2 | The Derivative as a Function | Exercises | p.92 |
2.3 | Basic Differentiation Formulas | Exercises | p.105 |
2.4 | The Product and Quotient Rules | Exercises | p.112 |
2.5 | The Chain Rule | Exercises | p.120 |
2.6 | Implicit Differentiation | Exercises | p.127 |
2.7 | Related Rates | Exercises | p.132 |
2.8 | Linear Approximations and Differentials | Exercises | p.138 |
Chapter 2 Review (Concept Check) | p.140 | ||
Chapter 2 Review (True-False Quiz) | p.140 | ||
Chapter 2 Review (Exercises) | p.141 |
Inverse Functions
3.1 | Exponential Functions | Exercises | p.150 |
3.2 | Inverse Functions and Logarithms | Exercises | p.161 |
3.3 | Derivatives of Logarithmic and Exponential Functions | Exercises | p.169 |
3.4 | Exponential Growth and Decay | Exercises | p.177 |
3.5 | Inverse Trigonometric Functions | Exercises | p.183 |
3.6 | Hyperbolic Functions | Exercises | p.189 |
3.7 | Indeterminate Forms and L'H么pital's Rule | Exercises | p.197 |
Chapter 3 Review (Concept Check) | p.199 | ||
Chapter 3 Review (True-False Quiz) | p.199 | ||
Chapter 3 Review (Exercises) | p.200 |
Applications Of Differentiation
4.1 | Maximum and Minimum Values | Exercises | p.208 |
4.2 | The Mean Value Theorem | Exercises | p.215 |
4.3 | Derivatives and the Shapes of Graphs | Exercises | p.222 |
4.4 | Curve Sketching | Exercises | p.230 |
4.5 | Optimization Problems | Exercises | p.238 |
4.6 | Newton's Method | Exercises | p.245 |
4.7 | Antiderivatives | Exercises | p.252 |
Chapter 4 Review (Concept Check) | p.253 | ||
Chapter 4 Review (True-False Quiz) | p.254 | ||
Chapter 4 Review (Exercises) | p.254 |
Integrals
5.1 | Areas and Distances | Exercises | p.266 |
5.2 | The Definite Integral | Exercises | p.279 |
5.3 | Evaluating Definite Integrals | Exercises | p.289 |
5.4 | The Fundamental Theorem of Calculus | Exercises | p.298 |
5.5 | The Substitution Rule | Exercises | p.306 |
Chapter 5 Review (Concept Check) | p.308 | ||
Chapter 5 Review (True-False Quiz) | p.308 | ||
Chapter 5 Review (Exercises) | p.309 |
Techniques Of Integration
6.1 | Integration by Parts | Exercises | p.316 |
6.2 | Trigonometric Integrals and Substitutions | Exercises | p.326 |
6.3 | Partial Fractions | Exercises | p.334 |
6.4 | Integration with Tables and Computer Algebra Systems | Exercises | p.340 |
6.5 | Approximate Integration | Exercises | p.350 |
6.6 | Improper Integrals | Exercises | p.360 |
Chapter 6 Review (Concept Check) | p.362 | ||
Chapter 6 Review (True-False Quiz) | p.362 | ||
Chapter 6 Review (Exercises) | p.363 |
Applications Of Integration
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7.1 | Areas between Curves | Exercises | p.369 |
7.2 | Volumes | Exercises | p.378 |
7.3 | Volumes by Cylindrical Shells | Exercises | p.384 |
7.4 | Arc Length | Exercises | p.391 |
7.5 | Area of a Surface of Revolution | Exercises | p.397 |
7.6 | Applications to Physics and Engineering | Exercises | p.408 |
7.7 | Differential Equations | Exercises | p.418 |
Chapter 7 Review (Concept Check) | p.421 | ||
Chapter 7 Review (Exercises) | p.422 |
Series
8.1 | Sequences | Exercises | p.434 |
8.2 | Series | Exercises | p.443 |
8.3 | The Integral and Comparison Tests | Exercises | p.452 |
8.4 | Other Convergence Tests | Exercises | p.463 |
8.5 | Power Series | Exercises | p.468 |
8.6 | Representing Functions as Power Series | Exercises | p.474 |
8.7 | Taylor and Maclaurin Series | Exercises | p.487 |
8.8 | Applications of Taylor Polynomials | Exercises | p.494 |
Chapter 8 Review (Concept Check) | p.497 | ||
Chapter 8 Review (True-False Quiz) | p.497 | ||
Chapter 8 Review (Exercises) | p.498 |
Parametric Equations And Polar Coordinates
9.1 | Parametric Curves | Exercises | p.505 |
9.2 | Calculus with Parametric Curves | Exercises | p.513 |
9.3 | Polar Coordinates | Exercises | p.522 |
9.4 | Areas and Lengths in Polar Coordinates | Exercises | p.528 |
9.5 | Conic Sections in Polar Coordinates | Exercises | p.534 |
Chapter 9 Review (Concept Check) | p.535 | ||
Chapter 9 Review (True-False Quiz) | p.535 | ||
Chapter 9 Review (Exercises) | p.535 |
Vectors And The Geometry Of Space
10.1 | Three-Dimensional Coordinate Systems | Exercises | p.541 |
10.2 | Vectors | Exercises | p.549 |
10.3 | The Dot Product | Exercises | p.556 |
10.4 | The Cross Product | Exercises | p.564 |
10.5 | Equations of Lines and Planes | Exercises | p.572 |
10.6 | Cylinders and Quadric Surfaces | Exercises | p.579 |
10.7 | Vector Functions and Space Curves | Exercises | p.589 |
10.8 | Arc Length and Curvature | Exercises | p.598 |
10.9 | Motion in Space: Velocity and Acceleration | Exercises | p.608 |
Chapter 10 Review (Concept Check) | p.610 | ||
Chapter 10 Review (True-False Quiz) | p.611 | ||
Chapter 10 Review (Exercises) | p.612 |
Partial Derivatives
11.1 | Functions and Several Variables | Exercises | p.623 |
11.2 | Limits and Continuity | Exercises | p.632 |
11.3 | Partial Derivatives | Exercises | p.638 |
11.4 | Tangent Places and Linear Approximations | Exercises | p.648 |
11.5 | The Chain Rule | Exercises | p.656 |
11.6 | Directional Derivatives and the Gradient Vector | Exercises | p.667 |
11.7 | Maximum and Minimum Values | Exercises | p.675 |
11.8 | Lagrange Multipliers | Exercises | p.683 |
Chapter 11 Review (Concept Check) | p.685 | ||
Chapter 11 Review (True-False Quiz) | p.685 | ||
Chapter 11 Review (Exercises) | p.686 |
Multiple Integrals
12.1 | Double Integrals over Rectangles | Exercises | p.698 |
12.2 | Double Integrals over General Regions | Exercises | p.707 |
12.3 | Double Integrals in Polar Coordinates | Exercises | p.713 |
12.4 | Applications of Double Integrals | Exercises | p.720 |
12.5 | Triple Integrals | Exercises | p.728 |
12.6 | Triple Integrals in Cylindrical Coordinates | Exercises | p.734 |
12.7 | Triple Integrals in Spherical Coordinates | Exercises | p.740 |
12.8 | Change of Variables in Multiple Integrals | Exercises | p.749 |
Chapter 12 Review (Concept Check) | p.751 | ||
Chapter 12 Review (True-False Quiz) | p.751 | ||
Chapter 12 Review (Exercises) | p.752 |
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13.1 | Vector Fields | Exercises | p.760 |
13.2 | Line Integral | Exercises | p.770 |
13.3 | The Fundamental Theorem for Line Integrals | Exercises | p.780 |
13.4 | Green's Theorem | Exercises | p.787 |
13.5 | Curl and Divergence | Exercises | p.795 |
13.6 | Parametric Surfaces and Their Areas | Exercises | p.805 |
13.7 | Surface Integrals | Exercises | p.816 |
13.8 | Stoke's Theorem | Exercises | p.822 |
13.9 | The Divergence Theorem | Exercises | p.829 |
Chapter 13 Review (Concept Check) | p.830 | ||
Chapter 13 Review (True-False Quiz) | p.831 | ||
Chapter 13 Review (Exercises) | p.831 |