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Unit 1

# 1.7 Selecting Procedures for Determining Limits

Anusha Tekumulla

### AP Calculus AB/BCΒ βΎοΈ

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## Selecting Procedures for Determining Limits

π₯Watch: AP Calculus AB/BC - Algebraic Limits
In this topic, we will discuss how to choose a method to determine a limit. So far, weβve learned about multiple ways to determine limits: direct substitution, factoring, and trigonometric identities. But how will you know when to use each of them? Take a look at the flowchart below to better understand when to use each method.

## Resources:

As we discussed before, the first thing you should do is use direct substitution. This is the easiest and simplest way to determine a limit. While you might be able to solve a limit using a more complicated method, you should always try to use direct substitution first.Β π΅
As the flowchart states, you can get three outcomes with direct substitution:Β
1. If you use direct substitution and you get a number, this is most likely the limit. However, you should still look at the graph of the function around the x value to be sure.Β π―
2. If you get b/0 when using direct substitution and b isnβt 0, then you most likely have an asymptote. After confirming that there is an asymptote, you can conclude that the limit does not exist.Β β
3. If you get 0/0, you have an indeterminate form and you must use either factoring, conjugates, or trig identities to solve the limit. Remember that indeterminate forms are things like 0/0 or β/β.Β β
If after trying factoring, conjugates, or trig identities you still cannot come up with an answer, the best thing to do is approximate the limit.Β π
Β

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