## Continuity Rule

### The continuity rule is a concept in mathematics that describes the behavior of functions

The continuity rule is a concept in mathematics that describes the behavior of functions. It states that if a function is continuous at each point within a certain interval, then it is also continuous over the entire interval.

More formally, let’s consider a function f(x). The continuity rule states that if the function is continuous at any value a within an interval (a, b), and it is also continuous at any value b, then it is continuous for all values x in the interval (a, b).

In other words, for a function to be continuous over an interval, it must be continuous at every point within that interval.

To determine if a function is continuous at a specific point, several conditions need to be satisfied:

1. The function must be defined at that point. In other words, there shouldn’t be any gaps or undefined values in the function.

2. The limit of the function as x approaches the point from both the left and the right must exist and be finite.

3. The limit must be equal to the value of the function at that point.

If these conditions are met, then the function is considered continuous at that point.

The continuity rule allows us to deduce the continuity of a function over a larger interval based on its continuity at specific points within that interval. It provides a useful tool for analyzing functions and understanding their behavior.

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