How to calculate multivariable limit using matlb?

I just want to know how to calculate multivarivabe limits? is there any special function? Please explain with an example.

Answer 1

[Uday Pradhan]

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!