Math Doubts

Limit of a function

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.

Introduction

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 $a$.

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

Example

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.

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