It cannot be denied that calculus is a difficult, important and well-studied subject. However, if you learn the basics in detail, you will not only grasp the more complex concepts but also find them quite fascinating. To understand machine learning algorithms, you need to have a good understanding of concepts such as the gradient of a function, the Hessians of a matrix, and optimization. Limits and the concept of continuity form the basis of all these issues. In this tutorial, you will discover how to calculate the limit of a function and how to determine if a function is continuous. After examining this study in detail, you will be able to: Determine if the function f(x) has a limit as x approaches a certain value Evaluate the limit of the function f(x) as x approaches a Determining whether a function is continuous at a point or an interval So let's start.

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**1. Evaluate each of the following limits :**