Barrons AP Calculus - David Bock

FIGURE N2–3

DEFINITION
The function f (x) is said to become infinite (positively or negatively) as x approaches c if f (x) can
be made arbitrarily large (positively or negatively) by taking x sufficiently close to c. We write

Since for the limit to exist it must be a finite number, neither of the preceding limits exists.
This definition can be extended to include x approaching c from the left or from the right. The
following examples illustrate these definitions.

EXAMPLE 4

Describe the behavior of near x = 0 using limits.

SOLUTION: The graph (Figure N2–4) shows that:

FIGURE N2–4