What Is Continuity In Maths?
Continuity is a property of functions that allows them to be “smooth.” This means that if you graph a function, it will be a smooth curve with no sudden jumps or breaks. Functions that are continuous can be differentiated and integrated easily, which is why they are so important in mathematics.
Continuity Of A Function
A function is continuous at a point if given any two points within the function’s domain, there exists a smooth curve that connects those points. A function is discontinuous at a point if there is a point within the function’s domain at which the function produces two different results.
Conditions for Continuity
A function is continuous at a point if it has a smooth curve at that point. This means that there is no break in the function at that point. The function must also be defined at that point.