Problem

Evaluate the limit

Solution

If we simply plug in –5 for t, we get 0/0, an indeterminate form. So we must be more clever in solving this problem. We can factor the numerator and the denominator of the fraction to get

This limit is the same as

since we must find the value approached when t is very close, but not equal, to –5. To evaluate this limit, we can plug in –5 for t to get

The two fractions differ only at a single point, where t = –5. The original fraction is not defined at this value, but the second fraction is defined, with value –3.5.