What Are Limits in Calculus?
The limit of a function is defined as the unique real number that the functions take when the variable of the function approaches a particular point. For any given function f(x), and a real number ‘c’, the limit of the function is defined as,
lim x ⇢ a f(x) = L
This is read as, “limit of f(x), as x approaches a equals L”
The image added below shows the function approaching the limit.
We can approach the limit of any function from two paths and the limit of the function exist only when both the individual limit of the function are equal. The two limits of the function are called Left Hand Limit(LHL) and the Right Hand Limit(RHL) of the function.
Limits Definition
To define the limit of a function let us consider a real-valued function “f” and the real number “a” such that the variable of the function approaches the value “a” then the limit is normally defined as:
lim x ⇢ a f(x) = L
It is read as “the limit of f of x, as x approaches a equals L”.
Formula Definition of Limit
The formula definition of the limit is given as,
For any function f(x) defined for all x ≠ aover an open interval containing a. Now suppose we have a real number L such that,
lim x ⇢ a f(x) = L
Then for every ε > 0, there exists a δ > 0, such that, 0 < |x – a| < δ the,
|f(x) – L| < ε
Limits in Calculus
Limits in maths are defined as the values approaching the output for the given input values of a function. Limits are used in calculus and mathematical analysis for finding the derivatives of the function. They are also used to define the continuity of the function.
The limit of any function is also used to find the integral of the function. The integral are of two types, Indefinite Integral, and Definite Integral, in definite integral we use the concept of upper limit and lower limit to find the answer to the definite integral. A function can reach a particular value from more than one path and the value of the function at that particular point is called the limit of the function at that point. Suppose we are given a function f(x) and when x approaches a the function approaches A this i represented using the limit as:
lim x ⇢ a f(x) = A
In this article, we will learn the introduction to limits, properties of limits, limits, and continuity, and others in detail.
Table of Content
- What Are Limits in Calculus?
- Limits Definition
- Formula of Limit
- Types of Limits
- Infinite Limits
- Limits at Infinity
- Properties of Limits
- Algebra of Limit
- Limits and Functions
- Limit of Polynomial Function
- Limit of Rational Function
- Limits of Complex Functions
- Limits of Exponential Functions
- Limit of a Function of Two Variables
- Calculating Limits
- Examples of Limits
- Limits and Derivatives Class 11
- Resources Related to Limits:
- Practice Questions on Limits in Calculus
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