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 concept in calculus that relates to the behavior of a function as it approaches a certain point. It states that if a function is continuous at a point c, then the limit of the function as x approaches c exists and is equal to the function value at c.
In other words, for a function f(x) to be continuous at a point c, three conditions must be met:
1. The function must be defined at c.
2. The limit of the function as x approaches c must exist.
3. The function value at c must be equal to the limit of the function as x approaches c.
The continuity rule is important in many areas of calculus, including differential equations and optimization. It allows for the analysis of functions that might otherwise be difficult to work with, and it enables us to make conclusions about the behavior of a function without directly evaluating its values at individual points.
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