The concept of limits is one of the fundamental building blocks of Calculus, enabling us to describe with precision how change in one variable affects change in another variable.
This chapter shows how to dine and calculate limits of function values. The calculation rules are straightforward, and most of the limits needed can be found by substitution, graphical investigation, numerical approximation, algebra, or some combination of these.
One of the uses of limits lies in building a careful definition of continuity. Continuous functions arise frequently in scientific work because they model such an enormous range of natural behaviorand because they have special mathematical properties.
(Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook Calculus - Graphical, Numerical, Algebraic.)