* PM Page 1 R E F E R E N C E PA G E 1 Cut here and keep for reference ALGEBRA GEOMETRY Arithmetic Operations Geometric Formulas a c ad bc b d bd a d ad b a c b c bc d ab ac a c b b b Formulas for area A, circumference C, and volume V: Triangle Circle Sector of Circle A 12 bh A 2 A 12 r C r s r in 12 ab sin a Exponents and Radicals xm x xn 1 n x x m x n x x m n x y x n y n n xn yn n n x s x m (s x )m n x s x n n n xy s xs y s n r h r s b r Sphere V 43 r 3 Cylinder V r 2h Cone V 13 r 2h A r 2 A rsr 2 h 2 n x x s n y sy r r h h Factoring Special Polynomials r x 2 y 2 x 3 y 3 2 xy y x 3 y 3 2 xy y Distance and Midpoint Formulas Binomial Theorem x 2 2xy y 2 x 2 2xy y 2 Distance between and 2, d 2 y2 x 3 3x 2 y 3xy 2 y 3 x 3 3x 2 y 3xy 2 y 3 x n nx where 2 x y 2 n k x y nxy y n k k n k 1 2 3 k Midpoint of P1 P2 : x1 x 2 y1 y2 , 2 2 Lines Slope of line through and 2, Quadratic Formula If ax 2 bx c 0, then x sb 2 4ac .*

Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

AM Page xii xii PREFACE Calculus, Seventh Edition, Hybrid Version, is similar to Calculus, Seventh Edition, in content and coverage except that all exercises are available only in Enhanced Web Assign. Essential Calculus is a much briefer book (800 pages), though it contains almost all of the topics in Calculus, Seventh Edition.

The relative brevity is achieved through briefer exposition of some topics and putting some features on the website.

The data in examples and exercises have been updated to be more timely.

Three new projects have been added: The Gini Index (page 429) explores how to measure income distribution among inhabitants of a given country and is a nice application of areas between curves.

9.4 Models for Population Growth 9.5 Linear Equations 9.6 Systems Review Problems Plus 603 604 605 616 622 629 633 Copyright 2010 Cengage Learning. May not be copied, scanned, or duplicated, in whole or in part.

AM Page vii CONTENTS 10 Parametric Equations and Polar Coordinates 635 10.1 Curves Defined Parametric Equations Laboratory Project 10.2 N Polar Coordinates Curves 645 653 N Families of Polar Curves 10.4 Areas and Lengths in Polar Coordinates 10.5 Conic Sections 10.6 Conic Sections in Polar Coordinates Review Problems Plus 644 654 Laboratory Project 11 Running Circles around Circles Calculus with Parametric Curves Laboratory Project 10.3 N 636 664 665 670 678 685 688 Infinite Sequences and Series 689 11.1 Sequences 690 Laboratory Project N Logistic Sequences 703 11.2 Series 703 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence and the Ratio and Root Tests 11.7 Strategy for Testing Series 11.8 Power Series 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 722 727 739 N N Review Problems Plus N 746 753 An Elusive Limit 767 How Newton Discovered the Binomial Series Applications of Taylor Polynomials Applied Project 732 741 Laboratory Project Writing Project 714 Radiation from the Stars 767 768 778 781 Copyright 2010 Cengage Learning. May not be copied, scanned, or duplicated, in whole or in part.

The coverage of topics is not encyclopedic and the material on transcendental functions and on parametric equations is woven throughout the book instead of being treated in separate chapters.

Calculus: Early Vectors introduces vectors and vector functions in the first semester and integrates them throughout the book.

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