Non zero over zero limits
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If g(x) is defined in an open interval that does not include -1, and g(x) gets closer and closer to 2, as x approaches -1, we write this as: Despite the presence of this hole, g(x) gets closer and closer to 2 as x gets closer and closer -1, as shown in the figure: So it looks like there is a hole in the function at x=-1. However, at (x = -1), the denominator is zero and we cannot divide by zero. If the denominator is not zero then g(x) can be simplified as: We can simplify the expression for g(x) as: We say that f(x) has a limit equal to 0, when x approaches -1.Įxtending the problem. We can see that f(x) gets closer and closer to 0 as x gets closer and closer -1, from either side of x=-1. Let’s start by looking at a simple function f(x) given by:
![non zero over zero limits non zero over zero limits](https://i.ytimg.com/vi/5AbDywZ9wds/hqdefault.jpg)
Photo by Mehreen Saeed, some rights reserved.
NON ZERO OVER ZERO LIMITS HOW TO
In this post, you will discover how to evaluate the limit of a function, and how to determine if a function is continuous or not.Īfter reading this post, you will be able to:ĭetermine if a function f(x) has a limit as x approaches a certain valueĮvaluate the limit of a function f(x) as x approaches aĭetermine if a function is continuous at a point or in an intervalĭetermine if the limit of a function exists for a certain pointĬompute the limit of a function for a certain pointĭetermine if a function is continuous at a point or within an intervalĪ Gentle Introduction to Limits and Continuity The concept of limits and continuity serves as a foundation for all these topics. To understand machine learning algorithms, you need to understand concepts such as gradient of a function, Hessians of a matrix, and optimization, etc. However, if you learn the fundamentals, you will not only be able to grasp the more complex concepts but also find them fascinating. There is no denying that calculus is a difficult subject.