Review Topics
Limits
For some functions, it is appropriate to look at their behavior from one side only. If
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
|
-
As x approaches 2 from the left, x − 2 is negative, and | x − 2|=− ( x − 2); hence,
-
As x approaches 2 from the right, x − 2 is positive, and | x − 2|= x − 2; hence;
-
Because
