*x*approaches

*c*from the right only, you write

or if *x* approaches *c* from the left only, you write

It follows, then, that if and only if

**Example 1:** Evaluate

Because *x* is approaching 0 from the right, it is always positive; is getting closer and closer to zero, so . Although substituting 0 for *x* would yield the same answer, the next example illustrates why this technique is not always appropriate.

**Example 2:** Evaluate .

Because *x* is approaching 0 from the left, it is always negative, and does not exist. In this situation, DNE. Also, note that DNE because .

**Example 3:** Evaluate

a. As *x* approaches 2 from the left, *x* − 2 is negative, and | *x* − 2|=− ( *x* − 2); hence,

b. As *x* approaches 2 from the right, *x* − 2 is positive, and | *x* − 2|= *x* − 2; hence;

c. Because