# An introduction to limits: Definition, formula, types, and
rules

In calculus, limits are frequently used to determine the values of the given functions at a specific point. It is widely used to define different branches of calculus like differentials, integrations, and continuity.

The limit can be finite or indeterminate,
for calculating the indeterminate function problems there is a rule of limit
known as L’hopital’s rule. The zero/zero, infinity by infinity, 0 power 0, etc.
are said to be indeterminate functions.

In this article, we will learn about the
definition, formula, types, rules, and examples of limits in calculus.

## What is the limit in calculus?

In calculus, a limit is a number
that a function approaches. Limits play a vital role in calculus for solving
complex problems and defining various kinds of calculus.

The derivative, integral, and continuity
used limits of calculus to find the differential, integral, and continuous
points of the functions. It is denoted by “lim” with a specific point at its
subscript.

### The formula of limit in calculus

The formula used to find the numerical result
of the function is given below.

It can be read
as the limit of the function g(z) as **z **approaches **v** is **N**.

### Types of limits in calculus

In calculus, limits have three kinds.

### Rules of limits

Here are some basic rules of limits.

** 1. ****Sum rule: **

**2. ****Constant rule**

**3. ****Constant function rule**

**4. ****Power rule**

**5. ****Difference rule:**

**6. ****Quotient rule:**

**7. ****Product rule:**

**8. ****L’hopital’s rule:**

## How to find limits?

Here are some solved examples of limits.

**Example 1**

Find the
limit of 12z^{2} – 13z + 4yz + 14z^{5} + 12, as z approaches to
4.

**Solution **

**Step 1:** Use the notation of
limit and write the function.

**Step 2:**
Apply the notation of limits separately to each
function by b using the sum, difference, and constant rule of limits.

**Step 3:** Write the constant
coefficients outside the limit notation by using the constant function rule of
limits.

**Step 4: **Now substitute 4 in the place of z
in the above expression.

You can also use a limit calculator with steps to avoid a large number of steps to get the result. Follow the below steps to use this tool.

**Step 1:** Enter the function.

**Step 2:** Select the variable.

**Step 3:** Select the type.

**Step 4:** Enter the limit value.

**Step 5:** Press the calculate button.

**Example 2**

Find the
limit of (2z^{2} + 3z + 19 - 19) / (12z – 2 + 2), as z approaches to 0.

**Solution **

**Step 1:** Use the notation of
limit and write the function.

**Step 2:**
Apply the notation of limits separately to each
function by b using the sum, difference, quotient, and constant rule of limits.

**Step 3:** Write the constant
coefficients outside the limit notation by using the constant function rule of
limits.

**Step 4: **Now substitute 0 in the place of z
in the above expression.

**Step 5:**
As the given function make an indeterminate form after
applying the limit, so apply the L’hopital’s rule.

## Summary

Now you can grab all the basics of limits in calculus from this post. We have discussed almost everything about the limit. You can solve y problem of limits easily by using the rules of limits.