Our Limit calculator instantly evaluates the limits of the given function. You can calculate left-hand, right-hand, or both-sided limits, with this limit calculator. Just enter your equation and get step by step solution using this limit solver with steps.

## What Is a Limit?

In mathematics:

**“A particular number that describes the behavior of a function for a given input”**

**Mathematically:**

$$\lim_{x\to\ b} f \left( x \right) = \text{L}$$

The limit of a function describes the behavior of the function near the point and not exactly the point itself.

## How To Evaluate Limits?

Let us resolve a few examples to help you make your limit calculations easy and fast!

### Example # 01

Solve the following right-hand limit with the steps involved:

$$\lim_{x \to 3^\mathtt{\text{+}}} \frac{10x^{2} - 5x - 13}{x^{2} - 52}$$

#### Solution

As the given function limit is

$$ \lim_{x \to 3^\mathtt{\text{+}}} \frac{10 x^{2} - 5 x - 13}{x^{2} - 52}$$

If you use this limit calculator, you will be getting fast results along with 100% accuracy. But if you want to master your manual computations as well, keep going through!

$$= \frac{10\left(3\right)^{2} - 5\left(3\right) - 13}{\left(3\right)^{2} - 52}$$

$$= \frac{10 * 9 - 15 - 13}{9 - 52}$$

$$= \frac{90-28}{-43}$$

$$= \frac{62}{-43}$$

$$= -1.441860$$

### Example # 02

Evaluate the following left-hand limit:

$$\lim_{x \to 4^\mathtt{\text{-}}} \cos^{3}{\left(x \right)}$$

#### Solution

$$ \lim_{x \to 4^\mathtt{\text{-}}} \cos^{3}{\left(x \right)}$$

$$ = \left(\cos^{3}{\left(4 \right)}\right)$$

This is the required limit calculation that could also be verified by the online multivariable limits calculator with steps.

## How To Use the Limit Calculator With Steps?

Using our calculator is very simple as it requires a few inputs to generate accurate results. Let’s have a look at these!

**Inputs:**

- Enter the function in its respective field and select the variable from the next list
- Set the limit value
- Select the direction of the limit
- Tap Calculate

**Outputs:**

- Limit evaluation
- Step-by-step calculations
- Taylor Series expansion at the determined limit
- Graph and Parsing Tree

## Faqs

### Does sin(x) Have a Limit?

No! When the value of variable x in sin(x) approaches infinity (∞), the value of y start oscillating between 0 and 1. This results in no definite limit evaluation for this trigonometric function and it can also be checked through our limit finder.

### What Is The Value of e^{∞}?

In mathematics, the alphabet e is an irrational number whose value is

$$e = 2.71 = 2.718281828459045…$$

If you compute the limit of this number either manually or through this online limit calculator, the answer will always be an irrational number again.

### Can There Be More Than One Limit To a Function?

Yes, a function may have more than one limit. One is where the variable reaches a limit value greater than the limit and vice versa. In such a case, the function is defined by its right–hand and left-hand limits that can also be determined through our limit solver with steps in seconds.

### Is Limit Equal To Function Value?

No, a limit can never be equal to its original function.

## References:

From the source Wikipedia: Limit (mathematics), Types of limits, Nonstandard analysis, (Continuity) of a function at a point, Properties