In this article, we will look closer at the functions with multiple variables. We have already seen what it means to take the limit of a function with a single variable, i.e., f(x). In this article, we will see how we can do it when we consider multiple variables.
Remembering the Rules
When we consider the limits of functions with a single variable, we have a few rules that can help us calculate them:
Translating to Multivariable Functions
We will now see that it is almost the same when we consider multivariable functions. We still have to use the same rules of calculating limits. Let us try to consider the case where we have a function with 2 variables: x and y. We then want to find the limit of it going towards a and b. It would look like so:
Let us try to take a few examples.
Imagine that we have the following multivariable function where we want to find the limit:
We can see that we need to use rules 2 and 3. We then have that:
Hence, we can see that the limit is equal to -5.
We can then try a more complicated example. So, let us imagine that we have the following:
