# How to calculate multivariable limit using matlb?

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Gaurav Shrivastava on 8 Jan 2021
I just want to know how to calculate multivarivabe limits? is there any special function? Please explain with an example.

Uday Pradhan on 15 Jan 2021
Hi Gaurav,
Unfortunately, there is no special function as of now that calculates multivariable limits directly.
However, there are a number of ways to investigate the limiting behaviour along a specific one - dimensional "path". For eg:
syms x y t f(x,y)
f(x,y) = x^3 * y / (x^6 + y^2); % we want to check limit of this as x and y approach 0
%Investigate limit along y = x path
limit(f(x,x),x,0)
This gives answer as 0. But along "y = x^3", we get:
>> limit(f(x,x^3),x,0)
ans =
1/2
So clearly the limit doesnot exists. You can also use limit function in a nested manner to calculate repeated limits as such:
limit(limit(f(x,y),x,0),y,0) ...(i)
limit(limit(f(x,y),y,0),x,0) ...(ii)
If both limits in (i) and (ii) exists and are NOT equal, then the double - limit does not exist. Of course, these workflows may not answer your query perfectly.
So, If you have a specific function that you are working on, you can post it as a reply to my answer. I will try to help you out, else, you can also post it as a separate question to reach a wider audience. Thanks!