# Strategy in finding limits

There are many techniques for finding limits that apply in various conditions. It's important to know all these techniques, but it's also important to know when to apply which technique.

Here's a handy dandy flow chart to help you calculate limits.

**Key point #1:**Direct substitution is the go-to method. Use other methods only when this fails, otherwise you're probably doing more work than you need to be. For example, it would be extra work to factor an expression into a simpler form if direct substitution would have worked without the factoring.

**Key point #2:**There's a big difference between getting $b/0$ and $0/0$ (where $b\neq 0$). When you get $b/0$, that indicates that the limit doesn't exist and is probably unbounded (an asymptote). In contrast, when you get $0/0$, that indicates that you don't have enough information to determine whether or not the limit exists, which is why it's called the

*indeterminate form*. If you wind up here, you've got more work to do, which is where the bottom half of the flow chart comes into play.

*Note: There's a powerful method for finding limits called l'Hôpital's rule, which you'll learn later on. It's not covered here because we haven't learned about derivatives yet.*