Limits Involving Infinity Section 1 4 Infinite Limits

Limits Involving Infinity Section 1. 4

Infinite Limits A limit in which f(x) increases or decreases without bound as x approaches c is called an infinite limit.

Saying the limit equals infinity or negative infinity, does not mean the limit exists. In fact, it means it doesn’t exist.

Definition of Vertical Asymptote If f(x) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a vertical asymptote of the graph of f.

Limits at Infinity (end behavior) If f(x) approaches L as x increases or decreases without bound, we say that f has a limit at infinity. These limits at infinity are denoted by

Definition of a Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f if

Theorem 3. 10 If r is a positive rational number and c is any real number, then Furthermore, if xr is defined when x < 0, then

Limits at Infinity (as x �±� ) and Rational Functions 1. If (degree of numerator) < (degree of denominator), then limit = 0. Horizontal Asymptote: y = 0 2. If (degree of numerator) = (degree of denominator), then limit = ratio of leading coefficients. Horizontal Asymptote: y = ratio of leading coef. 3. If (degree of numerator) > (degree of denominator), then limit = +�or -�. No Horizontal Asymptote