*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

This section contains 872 words(approx. 3 pages at 300 words per page) |

## Limit

The concept of limit is an essential component of **calculus**. Limits are typically the first idea of calculus that students study. Two fundamental concepts in calculus—the **derivative** and the **integral**—are based on the limit concept. Limits can be examined using three intuitive approaches: number sequences, functions, and geometric shapes.

## Number Sequences

One way to examine limits is through a sequence of numbers. The following example shows a sequence of numbers in which the limit is 0.

The second number in the sequence, ½, is the result of dividing the first number in the sequence, 1, by 2. The third number in the sequence, ¼, is the result of dividing the second number in the sequence, ½, by 2.

This process of dividing each number by 2 to acquire the next number in the sequence is continued in order to acquire each of the remaining values. The...

This section contains 872 words(approx. 3 pages at 300 words per page) |