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 three dots indicate that the sequence does not...