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

Email subscription

Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.