Math Doubts

Limits

The value of a function as the input approaches to some value is called limit.

Limit is a basic mathematical concept for learning calculus and it is useful determine continuity of function and also useful to study the advanced calculus topics derivatives and integrals.

Basics

There are two basic concepts to understand the concept of limits clearly in calculus.

  1. Approach
  2. The Limit
  3. Limit of a function

Representation

$x$ is a variable. A function is formed in terms of $x$ and it is written as $f{(x)}$ mathematically. The function $f{(x)}$ gives a value for every value of $x$. If $x = a$ then the value of function is $f{(a)}$.

Remember, the limit is not the value of function $f{(x)}$ when $x = a$, and it is a value of the function when the value of $x$ closer to $a$. The closer in calculus is denoted by symbol $\to$. Therefore, $x$ closer to $a$ is denoted by $x \to a$. It is read as $x$ tends to $a$ or $x$ approaches $a$.

In calculus, limit is symbolically represented by $\lim$. The limit of $f{(x)}$ is written as $\lim f{(x)}$ but the limit of function is calculated when $x$ approaches $a$. considering all factors, the limit of function $f{(x)}$ when $x$ tends to $a$ is written in mathematically as follows.

$\large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

Take the limit of function $f{(x)}$ is equal to $L$ when $x$ approaches $a$.

$L \,=\, \large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

One sided Limits

Learn how to find the left and right hand limits with understandable examples

Rules

Learn list of properties and standard results in limits to use them as formulas while evaluating the limit of any function in calculus.

Methods

The list of methods to learn how to find the limits of functions in calculus with understandable examples and worksheets for practice.

Problems

List of limits problems with solutions for leaning and practicing.

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved