Notice the graph can be drawn without lifting the pen from the paper. If we represent the function graphicly we get the following graph: We have the function defined on the interval as follow: įor better understanding let’s take a look at some examples: To say that the function continuous at the point, means that the limits of the function at the point is. Let be a function, let be its domain of definition, and let be a real number non isolated of there are no holes, breaks or gaps, of course, this definition isn’t a formal mathematical one but is used to simply explain the concept in an easy way.įor more formal, accurate, and a well mathematically put definition, we define the continuity of a function at a point as follow: Well, one of the simplest ways to define a continuous function is that a continuous function is any function that has the characteristic that its graph can be drawn with a pen without needing to lift the pencil from the page, so for a function to be continuous on a domain or an interval the graph must be one single curved line and having one part not multiple on this interval i.e. Next, we will proceed to learn about the discontinuity of a function alongside the different types of discontinuity, afterword we will introduce the theorem of intermediate values all this alongside taking a look at some illustrating examples in order to have a better understanding of the subject. In the previous article, we learned about how to study a function, and their domains of definition and codomains, a since we know that the domain of definition of a function is the set of possible values for which the function has an image or in other terms, but this may push ask some questions: does the graph of every function is formed of a single part or a single curved line?! Also, what about composite functions?!! How would their graphs look like, and does it always come in a signal part?!! Well, these questions and more will be answered by the end of this article.Īt first, we will learn about the idea of continuity with some simple and easy definitions in addition to some rigorous mathematical definitions of the continuity of a function on a domain or at a single point of its domain, after that, we will learn about the three conditions necessary to verify the continuity of a function at a point and the various properties of continuity.

Today we are taking a look at a new topic closely related to limits which is Continuity, in this article we will learn about the definition of continuity, how to determine if a function is continuous or not, and many more other things with some illustrating examples to grasp the content easily, now that we are eager to learn about continuity and with no further ado let the fun begin!!! Introduction We even learned about the interesting and strange Fun Facts – Infinity Facts, mysteries, paradoxes, and beyond in an entertaining blog post full of information, so make sure to check the previous article and to not miss any. Welcome again to another article!!! This time with a new article in Calculus, and the topic of our journey this time is Continuity so, after introducing the concept of limits of a function, their properties, and the different operations on limits alongside presenting the indeterminate forms that we may encounter when evaluating limits and how to deal with them and work around them in order to determine the limit in question. Important results and theorems about continuity.Continuity of some known continuous functions:.

Continuity of a function on an interval:.

The tree conditions of continuity at a point:.

Definition continuity calculus