Mendelson - Schaums outline of theory and problems of beginning calculus

ELLIOT MENDELSON is Professor Emeritus of Mathematics at Queens College of the City University of New York. He also has taught at the University of Chicago, Columbia University, and the University of Pennsylvania, and was a member of the Society of Fellows of Harvard University. He is the author of several books, including Schaums Outline of Boolean Algebra and Switching Circuits and Schaums 3000 Solved Problems in Calculus. His principal area of research is mathematical logic and set theory. Copyright 2008, 1997, 1985 by The McGraw-Hill Companies, Inc. All rights reserved.

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Every effort has been madeespecially in regard to the composition of the solved problemsto ease the beginners entry into calculus. There are also well over 1500 supplementary problems (with answers at the end of the book), and many new ones have been added for the Third Edition. In addition to college-level courses, secondary school courses in calculus can readily use this Outline. Many of the problems have been adapted from questions that have appeared in the Advanced Placement Examinations in Calculus, so that students will automatically receive preparation for those tests. A feature of the previous edition that has been carried over is the presence of problems that depend on the availability of graphing calculators. Such problems are preceded by the notation GC, enclosed in a square.

Solution of these problems is not necessary for comprehension of the text (except insofar as the use of a graphing calculator would enhance understanding of the subject). The author is grateful for the help of the many people who provided corrections and suggestions with respect to earlier editions, especially those offered by Frank Cannonito and M. F. Falus. He also wishes to thank the editor of this Third Edition, Charles Wall, as well as the editors of the previous editions, David Beckwith and Arthur Biderman.

Choose a point O on the line and call this point the origin. Now select a direction along ; say, the direction from left to right on the diagram. For every point P to the right of the origin O, let the coordinate of P be the distance between O and P. (Of course, to specify such a distance, it is first necessary to establish a unit distance by arbitrarily picking two points and assigning the number 1 to the distance between these two points.) In the diagram the distance is assumed to be 1, so that the coordinate of A is 1. The point B is two units away from O; therefore, B has coordinate 2. Every positive real number