# Multivariable Limit Calculator + Online Solver with Free Steps

The Multivariable Limit Calculator is an online calculator that is used to calculate the limits of functions with multiple variables. The Multivariable Limit Calculator allows the user to determine the limit of any function f(x) when the function is approached from multiple variables.

The Multivariable Limit Calculator is a professional mathematical calculator that provides accurate and speedy results in a matter of a few seconds. It takes the necessary input from the user and presents the solution in a detailed manner.

The Multivariable Limit Calculator is also free and does not require any cost for usage.

## What Is the Multivariable Limit Calculator?

The Multivariable Limit Calculator is a free online tool that is used to calculate the limit for any function f(x) when the function is approached from two variables, i.e, x and y.

The Multivariable Limit Calculator is very easy to use as it simply takes the input from the user into the designated input boxes and presents the solution in just a few seconds. The solution presented by the Multivariable Limit Calculator is always accurate.

The best feature of the Multivariable Limit Calculator is that it also identifies the functions for which the limit does not exist. In this way, the Multivariable Limit Calculator helps to identify the functions for which the limit does not exist in the particular domain.

The simple formula that the Multivariable Limit Calculator makes use of in determining the limits for functions f(x) is given below:

$\lim_{(x,y) \to (a,b)} f(x,y) = L$

If the limit cannot be determined through the direct approach, then the Multivariable Limit  Calculator also makes use of the path approach to determine if the limit even exists for the specified function.

In such a case, the limits obtained through the path approach for the given function must be equal for the multivariable limit of the function to exist.

L1 = L2

## How To Use the Multivariable Limit Calculator?

You can use this calculator by simply entering the function and specifying its variable of interest. The Multivariable Limit Calculator is fairly easy to use due to its extremely user-friendly interface. This calculator consists of a simple interface through which the user can easily navigate without any hassle to obtain the desired result.

The interface of the Multivariable Limit Calculator consists of three input boxes. The first input box has the title “Function” and it allows the user to enter in the specified function f(x) for which they wish to calculate the limit.

The second input box takes the multivariable from the user with respect to which the limit for the function f(x) needs to be calculated. This input box has the title “Variables (commas separated)” and it prompts the user to enter the variables. While entering the variables, make sure to separate them with a comma.

The third and the last input box has the title “Approaches” and it prompts the user to enter the domain from which you wish to approach your said function.

Lastly, the interface of the Multivariable Limit Calculator consists of a button that has the label “Submit” on which the user clicks once all the inputs have been filled. This button triggers the calculator to perform the solution.

For a better understanding of using the Multivariable Limit Calculator, consider the step-by-step guide given below.

### Step 1

First, before using the Multivariable Limit Calculator, analyze your function and your variables. Make sure to have at least two variables for determining the limit.

### Step 2

Now that you have analyzed your function, the next step is to enter the input. Fill in the first input box with the title “Function” with your specified function f(x).

### Step 3

Next up, move onto the second input box and insert your variables. Lastly, insert your domain into the last input box and you will have all your input boxes successfully filled.

### Step 4

Once you have entered all the input, the last step left is to click on the button that says “Submit.” Upon doing so, the Multivariable Limit Calculator will begin its processing and will present the solution after a few seconds.

## How Does the Multivariable Limit Calculator Works?

The Multivariable Limit Calculator works on the basic principle of calculus, which is limit computation. It takes the input from the user and computes the multivariable limit in just a few seconds. It also identifies the functions for which the limit does not exist.

For a better understanding of this working, let’s revise our previous concept of Multivariable Limits.

### What Is Multivariable Limit?

The Multivariable Limit is a fundamental concept in calculus in which the limits of such functions f(x) are calculated and are approached not from a single variable, like in most cases, but are approached from multiple variables.

So for such functions, the limit with respect to both the variables is determined. The multivariable limit can be expressed as follows:

$\lim_{(x,y) \to (a,b)} f(x,y) = L$

If the direct approach does not provide the limit, then the user may use the path approach to determine the limit. If the solutions obtained from the path approach do not match each other, then the limit does not exist for that function f(x).

## Solved Examples

For a more comprehensive understanding of the Multivariable Limit Calculator, consider the following example.

### Example 1

Find the limit if it exists for the following function:

$\lim_{(x,y) \to (-6,2)} xy cos(x+y)$

### Solution

Before beginning the solution, let’s first analyze our function. The function is given below:

$\lim_{(x,y) \to (-6,2)} xy cos(x+y)$

In this case, two variables are given, which are x and y, and the domain for the approach given is from -6 to 2.

Next up, insert the function f(x) into the first input box.

Insert the variables x and y into the second input box. Make sure to separate them with a comma.

Lastly, insert the approaches -6 and 2 into the third input box. Make sure to also separate them with a comma.

Once all the inputs have been inserted, click on the button that says “Submit.”

The calculator displays the following solution:

-12 cos(4)

Hence, the limit for the function f(x) does exist.