Limits and Continuity

Limits

 The limit of a function may be a confusing concept. What do we mean when we say that a function has a limit at a given point? And how can we estimate or compute limits?

Limit problems show up on both the Plus 2 and Engineering entrance examinations, so it’s important to understand the concepts and techniques in order to maximum your score. In this article I’ll define the limit of a function and illustrate a few techniques for evaluating them.

Continuity

The property of continuity is exhibited by various aspects of nature. The water flow in the rivers is continuous. The flow of time in human life is continuous i.e. you are getting older continuously. And so on. Similarly, in mathematics, we have the notion of the continuity of a function.

What it simply means is that a function is said to be continuous if you can sketch its curve on a graph without lifting your pen even once (provided that you can draw good). It is a very straightforward and close to accurate definition actually. But for the sake of higher mathematics, we must define it in a more precise way. That’s what we are going to do in this section. So let’s jump into it!

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