Limit Calculator

This online limit calculator instantly evaluates the limits of the entered function. If you want to calculate left-hand, right-hand, or both-sided limits, our calculator can be of great use. 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 the calculus 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 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