Epsilon-Delta Definition of a Limit

Definition

The epsilon-delta definition is a rigorous way to define limits in calculus. It states that for every positive value of epsilon (ε), there exists a positive value of delta (δ) such that if the distance between x and c is less than delta, then the distance between f(x) and L is less than epsilon.

Analogy

Imagine you want to get really close to your favorite celebrity at a concert. The epsilon-delta definition says that no matter how close you want to get (epsilon), there's always a point (delta) where you can stand so that you're within reach.

Related terms

Limits: In calculus, limits describe what happens as a function approaches a certain value or as x approaches infinity.

Continuity: A function is continuous if it has no breaks or jumps in its graph. This means it can be drawn without lifting your pencil from the paper.

Differentiability: A function is differentiable if it has a derivative at every point in its domain. The derivative represents the rate of change of the function.