In this topic, we will discuss how to choose a method to determine a limit. So far, we’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.
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. 🕵
As the flowchart states, you can get three outcomes with direct substitution:
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. 💯
If you get b/0 when using direct substitution and b isn’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. ✖
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 ∞/∞. ☑
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. 👌
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