*Sometimes easy and sometimes hard, our calculus problem of the week could come from any calculus topic. If you really want to get better at calculus, following these problems is a great way to make yourself practice! Past calculus problems of the week.*

**This week’s problem:
(click “see the solution” at the bottom of post to, well, see the solution.)**

This week we will go with a “routine” limit problem that highlights an aspect of limits people tend to forget!

Without using a graph, find the limit:

The “rule” I have for finding limits is to plug the number in unless something “breaks”. That is, plug the number in and see if I end up with a 0/0. If you try to plug in -1 in this case, you get . Many people at this stage would assume that the limit doesn’t exist, BUT THAT ISN’T NECESSARILY TRUE! 0/0 is an indeterminate form and getting it is a sign that you need to try another approach.

Luckily, the function we have simplifies nicely: . This means that .