Limit Definition

Definition

The limit definition provides a precise mathematical way to describe what happens as x approaches some value. It determines the behavior and value that a function approaches as its input gets arbitrarily close to a certain number.

Analogy

Imagine trying to hit a target with darts. As you throw darts closer and closer towards the bullseye, the limit is like the exact point you're trying to hit.

Related terms

Continuity: Continuity refers to a function that has no breaks, jumps, or holes in its graph. It can be defined using limits.

L'Hôpital's Rule: L'Hôpital's Rule is a technique used to evaluate limits involving indeterminate forms (such as 0/0 or ∞/∞) by taking derivatives of the numerator and denominator separately.

Squeeze Theorem: The squeeze theorem states that if two functions "squeeze" a third function between them and have the same limit at a certain point, then the squeezed function also has that limit at that point.