Limit Definition of Continuity
When the denominator (only) of f(x) equals zero
The limit definition of continuity is a way to mathematically describe a function’s continuity at a given point. It states that a function f(x) is continuous at a point x = a if and only if the limit of the function as x approaches a exists and is equal to the function value at a. Symbolically, this can be represented as:
lim x → a f(x) = f(a)
In other words, if the limit of f(x) as x approaches a exists and is equal to f(a), then the function f(x) is continuous at x = a. This means that the function has no abrupt changes or breaks at that point and can be drawn as a continuous curve without lifting the pencil.
The limit definition of continuity is often used in calculus to prove the continuity of functions at certain points. It is an important concept as it is the foundation for many important theorems in calculus, such as the Intermediate Value Theorem and the Mean Value Theorem.
More Answers:
The Derivative Of A Constant: Why D/Dx[C] = 0Mastering The Product Rule: How To Differentiate The Product Of Two Functions
C*X*U : Applying Product Rule To Find The Derivative