⏱️ **2 min read**

#discontinuities

written by

anusha tekumulla

published on march 23, 2020

Last updated on June 7, 2020

🎥**Watch: AP Calculus AB/BC - ****Continuity, Part II**

This is the first topic dealing with **continuity **in unit 1. Until this point, our main focus was limits and how to determine them. However, a large part in finding and determining limits is knowing whether or not the function is continuous at a certain point. In topics 1.9 - 1.13, we will discuss continuity and different types of discontinuities you will see on the AP Exam.

There are **four **types of discontinuities you have to know: **jump, point, essential, and removable. **

If the **left and right-handed limits aren’t equal**, then the double-handed limit does not exist (DNE). In this scenario, we would have a **jump discontinuity**. The graph of that would look something like this:

**Math Warehouse**

As you can see, there is a break in the physical continuity of the graph at x. If the limit from both sides is different, how can we find a specific value that the function approaches? We cannot. Thus, the limit **DNE**.

A **point discontinuity** occurs when the function has a “**hole**” in it from a mission point because the function has a value at that point that is “off the curve.”

**Wikipedia**

An** essential discontinuity** occurs when the curve has a **vertical asymptote.** This is also called an **infinite discontinuity. **

**Math Warehouse**

This last discontinuity is fairly common. A **removable discontinuity** occurs when you have a **rational expression** with a common factors in the numerator and denominator. Because these factors can be cancelled, the discontinuity is “removable.”

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