Limits of functions

Distinguish function values from limits and examine one-sided limits and limits at infinity.

Meaning

A function limit describes the value that outputs approach as inputs approach a given value. Whether the function is defined at that point is separate from the limit of nearby values.

Example

For so the limit as approaches 2 is 4. The original expression is undefined at but the limit exists.At a point approachable from both sides, the left-hand and right-hand limits must agree for a two-sided limit to exist. A zero denominator alone does not mean there is no limit.

Practice for this concept

Scope and references

Topics

Limits at a point, one-sided limits, limits at infinity

Learning goal

Distinguish function values from limits and examine one-sided limits and limits at infinity.

Helpful background

Review a function's domain and what it means for an input to approach a value.