What is a Limit in Mathematics?

A limit is the value that a function (or sequence) “approaches” as the input (or index) approaches some value.

Mathematically, for a function f(x), the limit of f(x) as approaches c is L, written as:

lim⁡_x→cf(x) = L

This means that for every ϵ > 0, there exists a δ>0 such that whenever 0 < ∣x − c∣ < δ, it follows that ∣f(x) − L∣ < ϵ.

Read More about Formal Definition of Limits.

Limits help us comprehend how functions behave as their inputs approach certain values. Think of a limit as the destination that a function aims to reach as the input gets closer and closer to a specific point.

In this article, we will explore the essential limit formulas that form the backbone of calculus. These formulas are like the rules of a game, guiding us on how to find limits in various scenarios. Whether you’re adding, subtracting, multiplying, or dividing functions, there are specific formulas to help you determine the limit.