The focus of this unit is the concept of a limit of a function and its relation to that of a continuous function. Various types of asymptotic behaviour of functions are defined, and there is a return to the topic of continuity, for which an alternative, but equivalent, definition is given. This unit also defines several unusual functions, and establishes their continuity properties. It shows that analogous definitions can be given of the 'limit' concepts. Finally uniform continuity is discussed, which plays an important role in the integration of continuous functions.