Infinite limit at infinity

Definition

An infinite limit at infinity describes the behavior of a function as it increases or decreases without bound as the input approaches positive or negative infinity. It indicates that the function grows arbitrarily large in magnitude.

5 Must Know Facts For Your Next Test

1. An infinite limit at infinity means the function does not approach a finite value but instead goes to positive or negative infinity.
2. Notation for an infinite limit at infinity includes $\lim_{{x \to \infty}} f(x) = \infty$ or $\lim_{{x \to -\infty}} f(x) = -\infty$.
3. The concept is often used to describe vertical asymptotes where the function values grow without bound near certain points.
4. Polynomial functions tend to have infinite limits at infinity if their leading term has a degree greater than zero.
5. Rational functions can have infinite limits at infinity depending on the degrees of the numerator and denominator.

Related terms

Limits: A fundamental concept in calculus that describes the value a function approaches as the input approaches some point.

Asymptote: A line that a graph of a function approaches but never touches.

Horizontal Asymptote:

A horizontal line that represents the value that a function approaches as x tends to plus or minus infinity.