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# Calculus Of A Single Variable

**by**Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

8th

### 9780618503032

061850303X

Hardcover

1/19/2005

Brooks Cole

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## Summary

Ideal for the single-variable, one-, or two-semester calculus course,Calculus of a Single Variable,8/e, contains the first 9 chapters ofCalculus,8/e. The text continues to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer a two-semesterCalculus I with Precalculustext. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best. The explanations, theorems, and definitions have been thoroughly and critically reviewed. Additionally, the exercise sets have been carefully and extensively examined to ensure they cover all calculus topics appropriately. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank. The Eduspace online resources have been integrated into a comprehensive learning system that combines numerous dynamic calculus resources with online homework and testing materials. Eduspace with eSolutions combines all the features of Eduspace with an electronic version of the textbook exercises and the complete solutions to the odd-numbered text exercises, providing students with a convenient and comprehensive way to do homework and view the course materials. The Integrated Learning System addresses the changing needs of today's instructors and students. Recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print, CD-ROM, and online formats. SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.

## Table of Contents

Preparation for Calculus | |

Graphs and Models | |

Linear Models and Rates of Change | |

Functions and Their Graphs | |

Fitting Models to Data | |

Limits and Their Properties | |

A Preview of Calculus | |

Finding Limits Graphically and Numerically | |

Evaluating Limits Analytically | |

Continuity and One-Sided Limits | |

Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

Product and Quotient Rules and Higher-Order Derivatives | |

The Chain Rule | |

Implicit Differentiation Section Project: Optical Illusions | |

Related Rates | |

Applications of Differentiation | |

Extrema on an Interval | |

Rolle\'s Theorem and the Mean Value Theorem | |

Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |

Concavity and the Second Derivative Test | |

Limits at Infinity | |

A Summary of Curve Sketching | |

Optimization Problems Section Project: Connecticut River | |

Newton\'s Method | |

Differentials | |

Integration | |

Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals | |

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |

Integration by Substitution | |

Numerical Integration | |

Logarithmic, Exponential, and Other Transcendental Functions | |

The Natural Logarithmic Function: Differentiation | |

The Natural Logarithmic Function: Integration | |

Inverse Functions | |

Exponential Functions: Differentiation and Integration | |

Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |

Inverse Trigonometric Functions: Differentiation | |

Inverse Trigonometric Functions: Integration | |

Hyperbolic Functions Section Project: St. Louis Arch | |

Differential Equations | |

Slope Fields and Euler\'s Method | |

Differential Equations: Growth and Decay | |

Separation of Variables and the Logistic Equation | |

First-Order Linear Differential Equations Section Project: Weight Loss | |

Applications of Integration | |

Area of a Region Between Two Curves | |

Volume: The Disk Method | |

Volume: The Shell Method Section Project: Saturn | |

Arc Length and Surfaces of Revolution | |

Work Section Project: Tidal Energy | |

Moments, Centers of Mass, and Centroids | |

Fluid Pressure and Fluid Force | |

Integration Techniques, L\'H?pital\'s Rule, and Improper Integrals | |

Basic Integration Rules | |

Integration by Parts | |

Trigonometric Integrals Section Project: Power Lines | |

Trigonometric Substitution | |

Partial Fractions | |

Integration by Tables and Other Integration Techniques | |

Indeterminate Forms and L\'H?pital\'s Rule 8.8 Improper Integrals | |

Infinite Series | |

Sequences | |

Series and Convergence Section Project: Cantor\'s Disappearing Table | |

The Integral Test and p-Series Section Project: The Harmonic Series | |

C | |

Table of Contents provided by Publisher. All Rights Reserved. |