# Multivariable Limit Calculator

## Multivariable Limit Calculator

Calculate the limit of a function f(x, y) as (x, y) approaches a specified point.

How to find the limit of a function with more than one variable? A **Multivariable Limit Calculator** helps you do just that. Enter the function and the point you want to approach into the calculator to find the limit.

### What is a Multivariable Limit?

A multivariable limit is the value that a function with two or more variables approaches as the variables get closer to a specific point. For example, the limit of $f(x,y)$ as $(x,y)$ approaches $(a,b)$.

### How To Use

Input Fields

**Function f(x, y):**Enter the mathematical function involving variables $x$ and $y$.**Point a (x-coordinate):**Input the x-coordinate of the point you are approaching.**Point b (y-coordinate):**Input the y-coordinate of the point you are approaching.

### Formula

Here is a basic outline of the formula and the variables involved:

Symbol | Description |
---|---|

$f(x,y)$ | Function of two variables $x$ and $y$ |

$a$ | x-coordinate of the point |

$b$ | y-coordinate of the point |

### Calculation Example

#### Example 1

For Example, the limit of the function $f(x,y)={x}^{2}+{y}^{2}$ as $(x,y)$approaches $(1,2)$.

**Step 1:**Identify the function $f(x,y)={x}^{2}+{y}^{2}$**Step 2:**Identify the point $(a,b)=(1,2)$**Step 3:**Substitute $x=1$ and $y=2$ into the function.$$f(1,2)={1}^{2}+{2}^{2}=1+4=5$$**Result:**The limit of $f(x,y)$ as $(x,y)$approaches $(1,2)$ is 5.

#### Example 2

Now, let’s find the limit of $f(x,y)=x\cdot y+y$as $(x,y)$approaches $(3,-1)$.

**Step 1:**Identify the function $f(x,y)=x\cdot y+y$**Step 2:**Identify the point $(a,b)=(3,-1)$**Step 3:**Substitute $x=3$and $y=-1$ into the function.$$f(3,-1)=3\cdot (-1)+(-1)=-3-1=-4$$**Result:**The limit of $f(x,y)$ as $(x,y)$approaches $(3,-1)$is -4.

The calculation of multivariable limits can be hard to understand for you but you can master with a right tool. I happy you liked the tool, In case you are facing any issue you reach us on report error page.