The limit of a function as its input approaches some value is expressed mathematically in a special form in calculus. So, let us learn how to write it in mathematical form for start studying the limits in calculus.

Let $x$ be a variable, $a$ be a constant and the function in terms of $x$ is written as $f(x)$. Mathematically, the operation of finding the limit of a function is simply denoted by a limiting operator $\lim$.

The limit of a function $f(x)$ as $x$ approaches $a$ is written in the following mathematical form.

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

Let $L$ be a value that represents the limit of the function $f(x)$ as $x$ tends to $a$.

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

Express the limit of a function $x^2-4$ as $x$ approaches $6$.

The given function is in terms of $x$. So, $f(x) = x^2-4$. Now, express it in limiting operation form for evaluating its limit as $x$ approaches $6$.

$L \,=\, \displaystyle \large \lim_{x \,\to\, 6}{\normalsize (x^2-4)}$

Thus, the limit of any function is mathematically expressed in calculus.

Latest Math Topics

Latest Math Problems

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

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

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved