Limits and Continuity

Abstract

In this example we illustrate an intuitive idea of a limit, leaving the precise definition until example 6. Consider the function:

$$ f(x) = \frac{{x - 1}}{{\sqrt x - 1}},\;(x \in {R^ + },x \ne 1) $$

The domain of definition excludes the point x = 1 because the expression (x = 1)/(√x = 1) gives the meaningless answer 0/0 when x = 1.