Continuity of functions is a mathematical concept that refers to the smoothness or unbrokenness of a function. It means that the function can be drawn without any breaks or gaps.
Continuity of functions is important because it allows us to make accurate predictions and interpretations of real-world phenomena. It also helps us to understand the behavior of a function and its graph.
To check for continuity of a function, we can use three main criteria: the function must be defined at the point in question, the limit of the function at that point must exist, and the value of the function at the point must be equal to the limit.
The three types of continuity of functions are point continuity, uniform continuity, and local continuity. Point continuity means that the function is continuous at a specific point. Uniform continuity means that the function is continuous over a specific interval. Local continuity means that the function is continuous at every point within a given interval.
Continuity of functions has many real-world applications, such as in physics to describe the motion of objects, in economics to analyze supply and demand curves, and in engineering to design and optimize structures and systems. It is also used in many other fields, including biology, chemistry, and computer science.