for the right-hand limit of f at c (as x approaches c through values greater than
c).
Example 1 __
The greatest-integer function g(x) = [x], shown in Figure N2–1, has different
left-hand and right-hand limits at every integer. For example,
This function, therefore, does not have a limit at x = 1 or, by the same reasoning,
at any other integer.
Figure N2–1However, [x] does have a limit at every nonintegral real number. For example,
Example 2 __
Suppose the function y = f (x), graphed in Figure N2–2, is defined as follows: