One-sided Limits
or if x approaches c from the left only, you writeIt follows, then, that 
if and only if 
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.
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 
.
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 
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