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In this article, we will get an easy-to-understand walkthrough of various subjects concerning limits. We will get the informal definition and use it to solve different limit calculations. In a future article, we will also look at the formal definition and use it to solve with. All of this is done to have a basic understanding of limits, such that we can draw upon this knowledge in the next two articles. These two articles will be looking at sequences and series and how we can find their point of convergence, i.e., their limit. We will start off this article by getting the informal definition of a limit since it’s the definition we will need to work with.
Defining a Limit
When we hear the word: ‘limit’, we might think about it as an edge of something — for example, our boundaries, a cliff, and so on. But when we talk about limits in a mathematical context, like in this article, we need to extend this definition a bit.
Imagine that we have a function, f(x). We won’t even bother to give a specific one, let us instead simply imagine that it looks like this:
Now, let us say that a limit can — very informally — be defined as:
The value which a function is working towards at a specific point.
