Let be a function defined at all values in an open interval containing , with the possible exception of itself, and let be a real number. If all values of the function approach the real number as the values of approach the number , then we say that the limit of as approaches is . (More succinct, as gets closer to , gets closer and stays close to .) Symbolically, we express this idea as
A function f(x)f(x) is said to be continuous at x=ax=a if
A function is said to be continuous on the interval [a,b][a,b] if it is continuous at each point in the interval.
The difference between the continuous and differentiable function is that the continuous function is a function, in which the curve obtained is a single unbroken curve. It means that the curve is not discontinuous. Whereas, the function is said to be differentiable if the function has a derivative.