Infinite Limit

Definition

An infinite limit occurs when a function approaches positive or negative infinity as x approaches a certain value. This means that as x gets closer to that value, f(x) grows without bound.

Analogy

Imagine you are climbing a mountain with an elevation sign at the top indicating an infinite height. As you hike up, the elevation keeps increasing until it becomes infinitely high. The sign represents the infinite limit of the mountain's height.

Related terms

Vertical Asymptote: A vertical asymptote is a vertical line that a graph approaches but never touches or crosses.

Horizontal Asymptote: A horizontal asymptote is a horizontal line that a graph approaches as x goes to positive or negative infinity.

Exponential Growth/Decay: Exponential growth refers to situations where something increases rapidly over time, while exponential decay refers to situations where something decreases rapidly over time. Both involve functions with infinite limits.