(a)

(b)

(c)

(d)

Determine whether limits of f, if any, exist at

`(a) x = −2, (b) x = 0,`

(c) x = 2, (d) x = 4.

`Figure N2–2`

SOLUTIONS:

`, so the right-hand limit exists at x = −2, even though f is not`

defined at x = −2.

does not exist. Although f is defined at x = 0 (f (0) = 2), we observe

that whereas . For the limit to exist at a point, the left-

hand and right-hand limits must be the same.

. This limit exists because . Indeed, the limit

exists at x = 2 even though it is different from the value of f at 2 (f (2) = 0).

, so the left-hand limit exists at x = 4.

###### Example 3 **__**

**__**