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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.
Here are some of the many improvements that incorporated into this edition: Some material has been rewritten for greater clarity or for better motivation.
See, for instance, the introduction to maximum and minimum values on page 274, the introduction to series on page 703, and the motivation for the cross product on page 808.
equation of line with slope m and b: If a b, then a c b c. Due to electronic rights, some third party content may be suppressed from the e Book e Chapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.It is suitable for students taking Engineering and Physics courses concurrently with calculus.Brief Applied Calculus is intended for students in business, the social sciences, and the life sciences. The changes have resulted from talking with my colleagues and students at the University of Toronto and from reading journals, as well as suggestions from users and reviewers.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.Essential Calculus: Early Transcendentals resembles Essential Calculus, but the exponential, logarithmic, and inverse trigonometric functions are covered in Chapter 3.Calculus: Concepts and Contexts, Fourth Edition, emphasizes conceptual understanding even more strongly than this book. 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 .2a y2 y1 x 2 x1 equation of line through with slope m: Inequalities and Absolute Value y y1 If a b and b c, then a c. If a 0, then a a a means x a or x means x a means or x Circles Equation of the circle with center and radius r: y r 2 Copyright 2010 Cengage Learning. May not be copied, scanned, or duplicated, in whole or in part.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. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.