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 N2–1`

However, [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: