Introduction to Calculus

Joan Van Glabek

• Publisher: Collins Reference
• Year: 2011
• ISBN:
  9780062115034
• Topic: Aides à l'étude
• Subtopic: Placement avancé

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The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications, and integrals and their applications. This guide is an indispensable aid to helping make the complex theories of calculus understandable. Completely revised and updated by Dr. Joan Van Glabek, this book includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, illustrations, and examples.

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CHAPTER 1

Introductory Topics

This chapter contains a short review of some of the algebraic topics that will be encountered in the remainder of the book. We review the real number system, interval notation, solving inequalities, and graphing in the Cartesian plane.

REAL NUMBERS, INEQUALITIES AND ABSOLUTE VALUE

REAL NUMBERS

The study of calculus involves real numbers. The union of the set of rational numbers (numbers that can be written as a ratio of two integers) and the set of irrational numbers (numbers that cannot be written as a terminating or repeating decimal) is the set of real numbers.

Irrationals

Rationals

ORDER

Compare real numbers using the following symbols:

• < less than
• ≤ less than or equal to
• > greater than
• ≥ greater than or equal to

For example,

means

lies to the left of

on the number line.

INTERVAL NOTATION AND SET NOTATION

In this book, we use subsets of the real numbers as solutions to equations or inequalities. These subsets are usually described using either interval notation or set notation as demonstrated in the following table.

Interval Notation	Set Notation	Graph
(–1, 3)	{x: - 1 < x < 3}
[–1. 3]	{x: - 1 ≤ x ≤ 3}
(–1, 3]	{x: - 1 < x ≤ 3}
[–1, 3)	{x: - 1 ≤ x < 3}

Notice that a parenthesis corresponds to an endpoint...