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.
More Answers:
Mastering Calculus Limits: Understanding the Fundamental Limits of 1/x and sin(x)/xProving the Existence of Function Roots & Intercepts: A Step-by-Step Guide Using the Intermediate Value Theorem
How the Intermediate Value Theorem Works to Find Solutions to Equations
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded