# What is continuity at a point?

Explanation: The points of continuity are points where a function exists, that it has some real value at that point. Since the question emanates from the topic of ‘Limits’ it can be further added that a function exist at a point ‘a’ if limx→af(x) exists (means it has some real value.)

Just so, what is the definition of continuity at a point?

We can define continuity at a point on a function as follows: The function f is continuous at x = c if f (c) is defined and if. . In other words, a function is continuous at a point if the function’s value at that point is the same as the limit at that point.

what is continuity of a function? Definition of Continuity A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied: f(a) exists (i.e. the value of f(a) is finite) Limxa f(x) exists (i.e. the right-hand limit = left-hand limit, and both are finite)

One may also ask, what are the three conditions for continuity at a point?

For a function to be continuous at a point from a given side, we need the following three conditions:

• the function is defined at the point.
• the function has a limit from that side at that point.
• the one-sided limit equals the value of the function at the point.

What is the synonym of continuity?

continuity, persistence(noun) the property of a continuous and connected period of time. Synonyms: perseverance, tenacity, persistency, perseveration, persistence, doggedness, pertinacity, tenaciousness.