Limit Formula
The limit formula is used to calculate the derivative of a function. The limit is the value of the function approaches as the input approaches mentioned value. Limits are used as a way of making approximations used in the calculation as close as possible to the actual value of the quantity. Let us understand the limit formula in detail in the following section.
What Is the Limit Formula?
Limit describes the behavior of some quantity that depends on an independent variable, as that independent variable ‘approaches’ or ‘comes close to' a particular value. Here below is the limit formula to calculate the limit of a function.
\(\mathop {\lim }\limits_{x \to a} f(x) = A \)
where,
 f(x) is a function
 x is a variable approaching to value a
It is read as “the limit of a function of x equals A as and when x approaches a.” Let us have a look at a few solved examples to understand the limit formula better.

Example 1: Using the limit formula, find the value of \(\mathop {\lim }\limits_{x \to 2} x^2 + 5. \)
Solution:
Putting values in the limit formula,
\[\mathop {\lim }\limits_{x \to 2} x^2 + 5 = 2^2 + 5 = 9\]
Answer: The value of: \(\mathop {\lim }\limits_{x \to 2} x^2 + 5\) is 9.

Example 2: Find the value of: \(\mathop {\lim }\limits_{x \to 0} 3x^3 + 4x+ 5. \)
Solution:
Putting values in the limit formula,
\(\begin{align*}\mathop {\lim }\limits_{x \to 0} 3x^3 + 4x+ 5 &= 3(0)^3 + 4(0) + 5 \\ &= 5\end{align*} \)
Answer: The value of: \(\mathop {\lim }\limits_{x \to 0} 3x^3 + 4x+ 5\) is 5.