Continuity Rule
If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point.
The continuity rule is a mathematical concept that relates to the behavior of functions. It is the concept that describes what occurs when the limit of a function is equal to the value of a function at a given point. Essentially, it states that when a function is continuous at a point, the limit of the function at that point is the same as the value of the function at that point.
If a function is continuous, it means that it does not have any sudden breaks or jumps in value. In other words, the values of the function change smoothly and gradually as the input values change. An example of a function that is continuous would be a straight line or a smooth curve.
The continuity rule is important in calculus because it allows us to use limits to calculate values of functions at certain points. If a function is not continuous, we cannot find the value of the function at that point using limits alone.
In summary, the continuity rule is a fundamental concept in calculus that relates to the behavior of functions. It describes what happens when the limit of a function is equal to the value of the function at a given point and helps us calculate values of functions at certain points.
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