Summary of the Precise Definition of a Limit | Calculus I

Module 2: Limits

Summary of the Precise Definition of a Limit

Essential Concepts

The intuitive notion of a limit may be converted into a rigorous mathematical definition known as the epsilon-delta definition of the limit.
The epsilon-delta definition may be used to prove statements about limits.
The epsilon-delta definition of a limit may be used to find deltas algebraically.



epsilon-delta definition of the limit: $\underset{x\to a}{\lim}f(x)=L$ if for every $\varepsilon >0$ , there exists a $\delta >0$ such that if $0<|x-a|<\delta$ , then $|f(x)-L|<\varepsilon$

triangle inequality: If $a$ and $b$ are any real numbers, then $|a+b|\le |a|+|b|$