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Limits at Infinity

Definition

Limits at Infinity refer to the behavior of a function as the input approaches positive or negative infinity. It determines the value that a function approaches as its input becomes infinitely large or small.

Analogy

Imagine you are driving on a long straight road. As you keep driving, you notice that the road seems to stretch out endlessly in front of you. The limits at infinity are like the destination or final point that you approach as you drive further and further along this never-ending road.

Related terms

Horizontal Asymptotes: Horizontal asymptotes are horizontal lines that a function approaches as x approaches positive or negative infinity. They represent the long-term behavior of a function.

lim x->+infinity f(x) = +infinity: This term refers to the limit of a function as x approaches positive infinity, where the output (y-value) of the function becomes infinitely large.

Vertical Asymptotes: Vertical asymptotes occur when there is an infinite gap between two parts of a graph, usually due to division by zero. They represent values where the function's output tends towards positive or negative infinity.