Limits in Calculus

What is Limit in Calculus?

A limit in calculus is defined as a function that approaches a particular value as the independent variable of the function approaches a particular value.

What is Limit Formula?

Limit formula is the formula that is used to calculate the limit of the given function. Let’s take a function y = f(x) and we take a point x = a then limit of function f(x) is defined as,

Iimx→0 f(x) = f(a)

What is Limit of a Function Class 11?

A limit of a function f(x) is defined as a value, where the function reaches as the limit reaches some value.

When can Limit Not Exist?

If the Left Hand Limit and the right hand limit of the function are not equal then we say that limit of the function does to exist, i.e. limit does not exit if,

LHL ≠ RHL

How to Find Limit in Calculus?

Limit of the function is found by substituting the value of the function that the limit approaches if the limit exist. When the limit of the function does not exist then we first simplify the function and then find the limit of the function.

What is the use of Limit?

The limit of the function is used for various purposes that are,

  • Limits are used to find the limiting value of the function.
  • Limits are used to find the derivative of the function.
  • Limits are also used to define the integral value of the function, etc.

What are Three Types of Limits?

The three types of limits are,

  • Two-Sided Limits
  • One-Sided Limits
  • Infinite Limits


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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