ABSTRACT
In this chapter, we first discuss limit of a function, right-hand limit, left-hand limit, infinite limits, limits at infinity, sequential definition of limit, Cauchy’s criterion for finite limits and presented several results covering various properties of limits with examples. Next we discuss monotonic functions, continuous and discontinuous functions by giving several related results with examples. Then the notion of uniform continuity is discussed with results and examples. Finally, we give a brief discussion on continuity and uniform continuity in metric spaces. Several solved examples and chapter-end exercises are also included covering all topics discussed in the chapter.
