Definition of Continuity
If1. lim x→c f(x) exists.2. f(c) exists.3. lim x→c f(x) = f(c)then f(x) is continuous at c.
In mathematics, continuity is a fundamental concept that describes the behavior of a function. A function is said to be continuous at a point if the function’s value at that point is equal to the limit of the function as the input approaches that point. More formally, a function f(x) is continuous at a point x=a if and only if the following three conditions are satisfied:
1. f(a) is defined.
2. The limit of f(x) as x approaches a exists.
3. The limit of f(x) as x approaches a is equal to f(a).
Intuitively, continuity means that there are no sudden jumps or breaks in the function’s graph at the point in question. If a function is continuous over its entire domain, it is said to be a continuous function.
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