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:
limx→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.
Limit Formula
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.
Table of Content
- What is a Limit in Mathematics?
- Limit Formulas
- Basic Limit Formulas
- Trigonometric Limits
- L-hospital Rule
- Exponential Limits
- Logarithmic limits
- Important Limit Results
- Sample Problem
- Practice Problems
- FAQs